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2020-05-16
|
On the asymptotic stability of wave equations coupled by velocities of anti-symmetric type
|
In this paper, we study the asymptotic stability of two wave equations
coupled by velocities of anti-symmetric type via only one damping. We adopt the
frequency domain method to prove that the system with smooth initial data is
logarithmically stable, provided that the coupling domain and the damping
domain intersect each other. Moreover, we show, by an example, that this
geometric assumption of the intersection is necessary for 1-D case.
|
2005.07977v2
|
2020-05-27
|
On the blow-up of solutions to semilinear damped wave equations with power nonlinearity in compact Lie groups
|
In this note, we prove a blow-up result for the semilinear damped wave
equation in a compact Lie group with power nonlinearity $|u|^p$ for any $p>1$,
under suitable integral sign assumptions for the initial data, by using an
iteration argument. A byproduct of this method is the upper bound estimate for
the lifespan of a local in time solution. As a preliminary result, a local (in
time) existence result is proved in the energy space via Fourier analysis on
compact Lie groups.
|
2005.13479v2
|
2020-06-13
|
On the well-posedness of the damped time-harmonic Galbrun equation and the equations of stellar oscillations
|
We study the time-harmonic Galbrun equation describing the propagation of
sound in the presence of a steady background flow. With additional rotational
and gravitational terms these equations are also fundamental in helio- and
asteroseismology as a model for stellar oscillations. For a simple damping
model we prove well-posedness of these equations, i.e. uniqueness, existence,
and stability of solutions under mild conditions on the parameters (essentially
subsonic flows). The main tool of our analysis is a generalized Helmholtz
decomposition.
|
2006.07658v1
|
2020-06-22
|
Prediction of short time qubit readout via measurement of the next quantum jump of a coupled damped driven harmonic oscillator
|
The dynamics of the next quantum jump for a qubit [two level system] coupled
to a readout resonator [damped driven harmonic oscillator] is calculated. A
quantum mechanical treatment of readout resonator reveals non exponential short
time behavior which could facilitate detection of the state of the qubit faster
than the resonator lifetime.
|
2006.11950v1
|
2020-07-08
|
The interplay of critical regularity of nonlinearities in a weakly coupled system of semi-linear damped wave equations
|
We would like to study a weakly coupled system of semi-linear classical
damped wave equations with moduli of continuity in nonlinearities whose powers
belong to the critical curve in the $p-q$ plane. The main goal of this paper is
to find out the sharp conditions of these moduli of continuity which classify
between global (in time) existence of small data solutions and finite time
blow-up of solutions.
|
2007.04157v1
|
2020-07-09
|
Semi-uniform stability of operator semigroups and energy decay of damped waves
|
Only in the last fifteen years or so has the notion of semi-uniform
stability, which lies between exponential stability and strong stability,
become part of the asymptotic theory of $C_0$-semigroups. It now lies at the
very heart of modern semigroup theory. After briefly reviewing the notions of
exponential and strong stability, we present an overview of some of the best
known (and often optimal) abstract results on semi-uniform stability. We go on
to indicate briefly how these results can be applied to obtain (sometimes
optimal) rates of energy decay for certain damped second-order Cauchy problems.
|
2007.04711v1
|
2020-07-10
|
Quasi-periodic travelling waves for a class of damped beams on rectangular tori
|
This article concerns a class of beam equations with damping on rectangular
tori. When the generators satisfy certain relationship, by excluding some value
of two model parameters, we prove that such models admit small amplitude
quasi-periodic travelling wave solutions with two frequencies, which are
continuations of two rotating wave solutions with one frequency. This result
holds not only for an isotropic torus, but also for an anisotropic torus. The
proof is mainly based on a Lyapunov--Schmidt reduction together with the
implicit function theorem.
|
2007.05154v1
|
2020-07-24
|
A Framework to Control Inter-Area Oscillations with Local Measurement
|
Inter-area oscillations in power system limit of power transfer capability
though tie-lines. For stable operation, wide-area power system stabilizers are
deployed to provide sufficient damping. However, as the feedback is through a
communication network, it brings challenges such as additional communication
layer and cybersecurity issues. To address this, a framework for synthesizing
remote signal from local measurement as feedback in the wide-area power system
stabilizer is proposed. The remote signal is synthesized using different
variants of observers in a case study of two-area benchmark system. The
proposed framework can improve the damping of inter-area oscillations for
static output feedback controller. The presented framework should help to
design attack-resilient controller design in smart grid.
|
2007.12426v1
|
2020-07-24
|
Convergence Rates of Inertial Primal-Dual Dynamical Methods for Separable Convex Optimization Problems
|
In this paper, we propose a second-order continuous primal-dual dynamical
system with time-dependent positive damping terms for a separable convex
optimization problem with linear equality constraints. By the Lyapunov function
approach, we investigate asymptotic properties of the proposed dynamical system
as the time $t\to+\infty$. The convergence rates are derived for different
choices of the damping coefficients. We also show that the obtained results are
robust under external perturbations.
|
2007.12428v1
|
2020-08-17
|
Dynamics of spatially indistinguishable particles and entanglement protection
|
We provide a general framework which allows one to obtain the dynamics of $N$
noninteracting spatially indistinguishable particles locally coupled to
separated environments. The approach is universal, being valid for both bosons
and fermions and for any type of system-environment interaction. It is then
applied to study the dynamics of two identical qubits under paradigmatic
Markovian noises, such as phase damping, depolarizing and amplitude damping. We
find that spatial indistinguishability of identical qubits is a controllable
intrinsic property of the system which protects quantum entanglement against
detrimental noise.
|
2008.07471v1
|
2020-09-02
|
Discriminating qubit amplitude damping channels
|
We address the issue of the discrimination between two-qubit amplitude
damping channels by exploring several strategies. For the single-shot, we show
that the excited state does not always give the optimal input, and that side
entanglement assistance has limited benefit. On the contrary, feedback
assistance from the environment is more beneficial. For the two-shot, we prove
the in-utility of entangled inputs. Then focusing on individual (local)
measurements, we find the optimal adaptive strategy.
|
2009.01000v3
|
2020-09-03
|
Asymptotic behavior of 2D stably stratified fluids with a damping term in the velocity equation
|
This article is concerned with the asymptotic behavior of the two-dimensional
inviscid Boussinesq equations with a damping term in the velocity equation.
Precisely, we provide the time-decay rates of the smooth solutions to that
system. The key ingredient is a careful analysis of the Green kernel of the
linearized problem in Fourier space, combined with bilinear estimates and
interpolation inequalities for handling the nonlinearity.
|
2009.01578v2
|
2020-08-05
|
The perturbational stability of the Schr$\ddot{o}$dinger equation
|
By using the Wigner transform, it is shown that the nonlinear
Schr$\ddot{\textmd{o}}$dinger equation can be described, in phase space, by a
kinetic theory similar to the Vlasov equation which is used for describing a
classical collisionless plasma. In this paper we mainly show Landau damping in
the quantum sense, namely,quantum Landau damping exists for the Wigner-Poisson
system. At the same time, we also prove the existence and the stability of the
nonlinear Schr$\ddot{\textmd{o}}$dinger equation under the quantum stability
assumption.
|
2009.09855v1
|
2020-10-12
|
Long time behavior of solutions for a damped Benjamin-Ono equation
|
We consider the Benjamin-Ono equation on the torus with an additional damping
term on the smallest Fourier modes (cos and sin). We first prove global
well-posedness of this equation in $L^2_{r,0}(\mathbb{T})$. Then, we describe
the weak limit points of the trajectories in $L^2_{r,0}(\mathbb{T})$ when time
goes to infinity, and show that these weak limit points are strong limit
points. Finally, we prove the boundedness of higher-order Sobolev norms for
this equation. Our key tool is the Birkhoff map for the Benjamin-Ono equation,
that we use as an adapted nonlinear Fourier transform.
|
2010.05520v1
|
2020-10-18
|
Classical limit of quantum mechanics for damped driven oscillatory systems: Quantum-classical correspondence
|
The investigation of quantum-classical correspondence may lead to gain a
deeper understanding of the classical limit of quantum theory. We develop a
quantum formalism on the basis of a linear-invariant theorem, which gives an
exact quantum-classical correspondence for damped oscillatory systems that are
perturbed by an arbitrary force. Within our formalism, the quantum trajectory
and expectation values of quantum observables are precisely coincide with their
classical counterparts in the case where we remove the global quantum constant
h from their quantum results. In particular, we illustrate the correspondence
of the quantum energy with the classical one in detail.
|
2010.08971v1
|
2020-10-21
|
Initial boundary value problem for a strongly damped wave equation with a general nonlinearity
|
In this paper, a strongly damped semilinear wave equation with a general
nonlinearity is considered. With the help of a newly constructed auxiliary
functional and the concavity argument, a general finite time blow-up criterion
is established for this problem. Furthermore, the lifespan of the weak solution
is estimated from both above and below. This partially extends some results
obtained in recent literatures and sheds some light on the similar effect of
power type nonlinearity and logarithmic nonlinearity on finite time blow-up of
solutions to such problems.
|
2010.10696v1
|
2020-10-21
|
MRI Image Recovery using Damped Denoising Vector AMP
|
Motivated by image recovery in magnetic resonance imaging (MRI), we propose a
new approach to solving linear inverse problems based on iteratively calling a
deep neural-network, sometimes referred to as plug-and-play recovery. Our
approach is based on the vector approximate message passing (VAMP) algorithm,
which is known for mean-squared error (MSE)-optimal recovery under certain
conditions. The forward operator in MRI, however, does not satisfy these
conditions, and thus we design new damping and initialization schemes to help
VAMP. The resulting DD-VAMP++ algorithm is shown to outperform existing
algorithms in convergence speed and accuracy when recovering images from the
fastMRI database for the practical case of Cartesian sampling.
|
2010.11321v1
|
2020-11-05
|
Mathematical modelling of an unstable bent flow using the selective frequency damping method
|
The selective frequency damping method was applied to a bent flow. The method
was used in an adaptive formulation. The most dangerous frequency was
determined by solving an eigenvalue problem. It was found that one of the
patterns, steady-state or pulsating, may exist at some relatively high Reynolds
numbers. The periodic flow occurs due to the instability of the steady-state
flow. This numerical method is easy to use but requires a great deal of time
for calculations.
|
2011.02646v1
|
2020-11-04
|
The "Dark disk" model in the light of DAMPE experiment
|
There are a lot of models considering the Dark Matter (DM) to be the origin
of cosmic ray (CR) positron excess. However, they face an obstacle in the form
of gamma-rays. Simple DM models tend to overproduce gamma-rays, leading to
contradiction with isotropic gamma-ray background (IGRB). The <<dark disk>>
model has been proposed to alleviate this contradiction. This work considers
results of DAMPE experiment in the framework of the disk model. It is obtained
that such a framework allows improving data fit considerably.
|
2011.04425v2
|
2020-12-15
|
On the stability of Bresse system with one discontinuous local internal Kelvin-Voigt damping on the axial force
|
In this paper, we investigate the stabilization of a linear Bresse system
with one discontinuous local internal viscoelastic damping of Kelvin-Voigt type
acting on the axial force, under fully Dirichlet boundary conditions. First,
using a general criteria of Arendt-Batty, we prove the strong stability of our
system. Finally, using a frequency domain approach combined with the multiplier
method, we prove that the energy of our system decays polynomially with
different rates.
|
2012.08219v1
|
2020-12-28
|
An efficient method for approximating resonance curves of weakly-damped nonlinear mechanical systems
|
A method is presented for tracing the locus of a specific peak in the
frequency response under variation of a parameter. It is applicable to
periodic, steady-state vibrations of harmonically forced nonlinear mechanical
systems. It operates in the frequency domain and its central idea is to assume
a constant phase lag between forcing and response. The method is validated for
a two-degree-of-freedom oscillator with cubic spring and a bladed disk with
shroud contact. The method provides superior computational efficiency, but is
limited to weakly-damped systems. Finally, the capability to reveal isolated
solution branches is highlighted.
|
2012.14458v1
|
2021-01-16
|
Convergence of non-autonomous attractors for subquintic weakly damped wave equation
|
We study the non-autonomous weakly damped wave equation with subquintic
growth condition on the nonlinearity. Our main focus is the class of
Shatah--Struwe solutions, which satisfy the Strichartz estimates and are
coincide with the class of solutions obtained by the Galerkin method. For this
class we show the existence and smoothness of pullback, uniform, and cocycle
attractors and the relations between them. We also prove that these
non-autonomous attractors converge upper-semicontinuously to the global
attractor for the limit autonomous problem if the time-dependent nonlinearity
tends to time independent function in an appropriate way.
|
2101.06523v1
|
2021-01-20
|
A Damped Newton Algorithm for Generated Jacobian Equations
|
Generated Jacobian Equations have been introduced by Trudinger [Disc. cont.
dyn. sys (2014), pp. 1663-1681] as a generalization of Monge-Amp{\`e}re
equations arising in optimal transport. In this paper, we introduce and study a
damped Newton algorithm for solving these equations in the semi-discrete
setting, meaning that one of the two measures involved in the problem is
finitely supported and the other one is absolutely continuous. We also present
a numerical application of this algorithm to the near-field parallel refractor
problem arising in non-imaging problems.
|
2101.08080v1
|
2021-02-04
|
Global existence results for semi-linear structurally damped wave equations with nonlinear convection
|
In this paper, we consider the Cauchy problem for semi-linear wave equations
with structural damping term $\nu (-\Delta)^2 u_t$, where $\nu >0$ is a
constant. As being mentioned in [8,10], the linear principal part brings both
the diffusion phenomenon and the regularity loss of solutions. This implies
that, for the nonlinear problems, the choice of solution spaces plays an
important role to obtain global solutions with sharp decay properties in time.
Our main purpose of this paper is to prove the global (in time) existence of
solutions for the small data and their decay properties for the supercritical
nonlinearities.
|
2102.02445v2
|
2021-02-14
|
Suppression of singularities of solutions of the Euler-Poisson system with density-dependent damping
|
We find a sharp condition on the density-dependent coefficient of damping of
a one-dimensional repulsive Euler-Poisson system, which makes it possible to
suppress the formation of singularities in the solution of the Cauchy problem
with arbitrary smooth data. In the context of plasma physics, this means the
possibility of suppressing the breakdown of arbitrary oscillations of cold
plasma.
|
2102.07176v2
|
2021-02-15
|
Piezoelectric beam with magnetic effect, time-varying delay and time-varying weights
|
The main result of this work is to obtain the exponential decay of the
solutions of a piezoelectric beam model with magnetic effect and delay term.
The dampings are inserted into the equation of longitudinal displacement. The
terms of damping, whose weight associated with them varies over time, are of
the friction type, and one of them has delay. This work will also address the
issue of existence and uniqueness of solution for the model.
|
2102.07538v1
|
2021-02-23
|
Effects of ground-state correlations on damping of giant dipole resonaces in $LS$ closed shell nuclei
|
The effects of ground-state correlations on the damping of isovector giant
dipole resonances in $LS$ closed shell nuclei $^{16}$O and $^{40}$Ca are
studied using extended random-phase-approximation (RPA) approaches derived from
the time-dependent density-matrix theory. It is pointed out that unconventional
two-body amplitudes of one particle--three hole and three particle--one hole
types which are neglected in most extended RPA theories play an important role
in the fragmentation of isovector dipole strength.
|
2102.11505v2
|
2021-02-28
|
The influence of the physical coefficients of a Bresse system with one singular local viscous damping in the longitudinal displacement on its stabilization
|
In this paper, we investigate the stabilization of a linear Bresse system
with one singular local frictional damping acting in the longitudinal
displacement, under fully Dirichlet boundary conditions. First, we prove the
strong stability of our system. Next, using a frequency domain approach
combined with the multiplier method, we establish the exponential stability of
the solution if and only if the three waves have the same speed of propagation.
On the contrary, we prove that the energy of our system decays polynomially
with rates $t^{-1}$ or $t^{-\frac{1}{2}}$.
|
2103.00628v2
|
2021-03-01
|
On a damped nonlinear beam equation
|
In this note we analyze the large time behavior of solutions to an
initial/boundary problem involving a damped nonlinear beam equation. We show
that under physically realistic conditions on the nonlinear terms in the
equation of motion the energy is a decreasing function of time and solutions
converge to a stationary solution with respect to a desirable norm.
|
2103.00969v3
|
2021-03-23
|
Fast convergence of dynamical ADMM via time scaling of damped inertial dynamics
|
In this paper, we propose in a Hilbertian setting a second-order
time-continuous dynamic system with fast convergence guarantees to solve
structured convex minimization problems with an affine constraint. The system
is associated with the augmented Lagrangian formulation of the minimization
problem. The corresponding dynamics brings into play three general time-varying
parameters, each with specific properties, and which are respectively
associated with viscous damping, extrapolation and temporal scaling. By
appropriately adjusting these parameters, we develop a Lyapunov analysis which
provides fast convergence properties of the values and of the feasibility gap.
These results will naturally pave the way for developing corresponding
accelerated ADMM algorithms, obtained by temporal discretization.
|
2103.12675v1
|
2021-03-29
|
Comparison between the Cauchy problem and the scattering problem for the Landau damping in the Vlasov-HMF equation
|
We analyze the analytic Landau damping problem for the Vlasov-HMF equation,
by fixing the asymptotic behavior of the solution. We use a new method for this
"scattering problem", closer to the one used for the Cauchy problem. In this
way we are able to compare the two results, emphasizing the different influence
of the plasma echoes in the two approaches. In particular, we prove a
non-perturbative result for the scattering problem.
|
2103.15932v2
|
2021-04-06
|
Realising Einstein's mirror: Optomechanical damping with a thermal photon gas
|
In 1909 Einstein described the thermalization of a mirror within a blackbody
cavity by collisions with thermal photons. While the time to thermalize the
motion of even a microscale or nanoscale object is so long that it is not
feasible, we show that it is using the high intensity light from an amplified
thermal light source with a well-defined chemical potential. We predict damping
of the center-of mass motion due to this effect on times scales of seconds for
small optomechanical systems, such as levitated nanoparticles, allowing
experimental observation.
|
2104.02708v2
|
2021-04-12
|
The pressureless damped Euler-Riesz equations
|
In this paper, we analyze the pressureless damped Euler-Riesz equations posed
in either $\mathbb{R}^d$ or $\mathbb{T}^d$. We construct the global-in-time
existence and uniqueness of classical solutions for the system around a
constant background state. We also establish large-time behaviors of classical
solutions showing the solutions towards the equilibrium as time goes to
infinity. For the whole space case, we first show the algebraic decay rate of
solutions under additional assumptions on the initial data compared to the
existence theory. We then refine the argument to have the exponential decay
rate of convergence even in the whole space. In the case of the periodic
domain, without any further regularity assumptions on the initial data, we
provide the exponential convergence of solutions.
|
2104.05153v1
|
2021-04-12
|
Fractional time stepping and adjoint based gradient computation in an inverse problem for a fractionally damped wave equation
|
In this paper we consider the inverse problem of identifying the initial data
in a fractionally damped wave equation from time trace measurements on a
surface, as relevant in photoacoustic or thermoacoustic tomography. We derive
and analyze a time stepping method for the numerical solution of the
corresponding forward problem. Moreover, to efficiently obtain reconstructions
by minimizing a Tikhonov regularization functional (or alternatively, by
computing the MAP estimator in a Bayesian approach), we develop an adjoint
based scheme for gradient computation. Numerical reconstructions in two space
dimensions illustrate the performance of the devised methods.
|
2104.05577v1
|
2021-04-15
|
Explaining Neptune's Eccentricity
|
Early migration damped Neptune's eccentricity. Here, we assume that the
damped value was much smaller than the value observed today, and show that the
closest flyby of $\sim 0.1 \; \mathrm{M_{\odot}}$ star over $\sim 4.5
\mathrm{\; Gyr}$ in the field, at a distance of $\sim 10^3 \mathrm{\; AU}$
would explain the value of Neptune's eccentricity observed today.
|
2104.07672v3
|
2021-04-17
|
Lifespan estimates for wave equations with damping and potential posed on asymptotically Euclidean manifolds
|
In this work, we investigate the problem of finite time blow up as well as
the upper bound estimates of lifespan for solutions to small-amplitude
semilinear wave equations with time dependent damping and potential, and mixed
nonlinearities $c_1 |u_t|^p+c_2 |u|^q$, posed on asymptotically Euclidean
manifolds, which is related to both the Strauss conjecture and the Glassey
conjecture.
|
2104.08497v2
|
2021-05-20
|
On the the critical exponent for the semilinear Euler-Poisson-Darboux-Tricomi equation with power nonlinearity
|
In this note, we derive a blow-up result for a semilinear generalized Tricomi
equation with damping and mass terms having time-dependent coefficients. We
consider these coefficients with critical decay rates. Due to this threshold
nature of the time-dependent coefficients (both for the damping and for the
mass), the multiplicative constants appearing in these lower-order terms
strongly influence the value of the critical exponent, determining a
competition between a Fujita-type exponent and a Strauss-type exponent.
|
2105.09879v2
|
2021-06-02
|
Convergent dynamics of optimal nonlinear damping control
|
Following Demidovich's concept and definition of convergent systems, we
analyze the optimal nonlinear damping control, recently proposed [1] for the
second-order systems. Targeting the problem of output regulation,
correspondingly tracking of $\mathcal{C}^1$-trajectories, it is shown that all
solutions of the control system are globally uniformly asymptotically stable.
The existence of the unique limit solution in the origin of the control error
and its time derivative coordinates are shown in the sense of Demidovich's
convergent dynamics. Explanative numerical examples are also provided along
with analysis.
|
2106.00962v1
|
2021-06-26
|
Role of Dissipation on the Stability of a Parametrically Driven Quantum Harmonic Oscillator
|
We study the dissipative dynamics of a single quantum harmonic oscillator
subjected to a parametric driving with in an effective Hamiltonian approach.
Using Liouville von Neumann approach, we show that the time evolution of a
parametrically driven dissipative quantum oscillator has a strong connection
with the classical damped Mathieu equation. Based on the numerical analysis of
the Monodromy matrix, we demonstrate that the dynamical instability generated
by the parametric driving are reduced by the effect of dissipation. Further, we
obtain a closed relationship between the localization of the Wigner function
and the stability of the damped Mathieu equation.
|
2106.14018v1
|
2021-07-11
|
Space-time arithmetic quasi-periodic homogenization for damped wave equations
|
This paper is concerned with space-time homogenization problems for damped
wave equations with spatially periodic oscillating elliptic coefficients and
temporally (arithmetic) quasi-periodic oscillating viscosity coefficients. Main
results consist of a homogenization theorem, qualitative properties of
homogenized matrices which appear in homogenized equations and a corrector
result for gradients of solutions. In particular, homogenized equations and
cell problems will turn out to deeply depend on the quasi-periodicity as well
as the log ratio of spatial and temporal periods of the coefficients. Even
types of equations will change depending on the log ratio and
quasi-periodicity. Proofs of the main results are based on a (very weak)
space-time two-scale convergence theory.
|
2107.04966v1
|
2021-07-29
|
Global existence for damped $σ$-evolution equations with nonlocal nonlinearity
|
In this research, we would like to study the global (in time) existence of
small data solutions to the following damped $\sigma$-evolution equations with
nonlocal (in space) nonlinearity: \begin{equation*}
\partial_{t}^{2}u+(-\Delta)^{\sigma}u+\partial_{t}u+(-\Delta)^{\sigma}\partial_{t}u=I_{\alpha}(|u|^{p}),
\ \ t>0, \ \ x\in \mathbb{R}^{n}, \end{equation*} where $\sigma\geq1$, $p>1$
and $I_{\alpha}$ is the Riesz potential of power nonlinearity $|u|^{p}$ for any
$\alpha\in (0,n)$. More precisely, by using the $(L^{m}\cap L^{2})-L^{2}$ and
$L^{2}-L^{2}$ linear estimates, where $m\in[1,2]$, we show the new influence of
the parameter $\alpha$ on the admissible ranges of the exponent $p$.
|
2107.13924v1
|
2021-08-17
|
Estimate of the attractive velocity of attractors for some dynamical systems
|
In this paper, we first prove an abstract theorem on the existence of
polynomial attractors and the concrete estimate of their attractive velocity
for infinite-dimensional dynamical systems, then apply this theorem to a class
of wave equations with nonlocal weak damping and anti-damping in case that the
nonlinear term~$f$~is of subcritical growth.
|
2108.07410v4
|
2021-08-27
|
Distributed Mirror Descent Algorithm with Bregman Damping for Nonsmooth Constrained Optimization
|
To solve distributed optimization efficiently with various constraints and
nonsmooth functions, we propose a distributed mirror descent algorithm with
embedded Bregman damping, as a generalization of conventional distributed
projection-based algorithms. In fact, our continuous-time algorithm well
inherits good capabilities of mirror descent approaches to rapidly compute
explicit solutions to the problems with some specific constraint structures.
Moreover, we rigorously prove the convergence of our algorithm, along with the
boundedness of the trajectory and the accuracy of the solution.
|
2108.12136v1
|
2021-08-27
|
Non relativistic and ultra relativistic limits in 2d stochastic nonlinear damped Klein-Gordon equation
|
We study the non relativistic and ultra relativistic limits in the
two-dimensional nonlinear damped Klein-Gordon equation driven by a space-time
white noise on the torus. In order to take the limits, it is crucial to clarify
the parameter dependence in the estimates of solution. In this paper we present
two methods to confirm this parameter dependence. One is the classical, simple
energy method. Another is the method via Strichartz estimates.
|
2108.12183v4
|
2021-09-08
|
The isothermal limit for the compressible Euler equations with damping
|
We consider the isothermal Euler system with damping. We rigorously show the
convergence of Barenblatt solutions towards a limit Gaussian profile in the
isothermal limit $\gamma$ $\rightarrow$ 1, and we explicitly compute the
propagation and the behavior of Gaussian initial data. We then show the weak L
1 convergence of the density as well as the asymptotic behavior of its first
and second moments. Contents 1. Introduction 1 2. Assumptions and main results
3 3. The limit $\gamma$ $\rightarrow$ 1 of Barenblatt's solutions 6 4. Gaussian
solutions 9 5. Evolution of certain quantities 10 6. Convergence 15 7.
Conclusion 17 References 17
|
2109.03590v1
|
2021-11-01
|
Strong solution of modified 3D-Navier-stockes equations
|
In this paper we study the incompressible Navier-Stokes equations with
logarithme damping {\alpha} log(e + |u|2)|u|2u, where we used new methods, new
tools and Fourier analysis
|
2111.00859v2
|
2021-11-02
|
Blow-up of solutions to semilinear wave equations with a time-dependent strong damping
|
The paper investigates a class of a semilinear wave equation with
time-dependent damping term ($-\frac{1}{{(1+t)}^{\beta}}\Delta u_t$) and a
nonlinearity $|u|^p$. We will show the influence of the the parameter $\beta$
in the blow-up results under some hypothesis on the initial data and the
exponent $p$ by using the test function method. We also study the local
existence in time of mild solution in the energy space $H^1(\mathbb{R}^n)\times
L^2(\mathbb{R}^n)$.
|
2111.01433v1
|
2021-11-02
|
Around plane waves solutions of the Schr{ö}dinger-Langevin equation
|
We consider the logarithmic Schr{\"o}dinger equations with damping, also
called Schr{\"o}dinger-Langevin equation. On a periodic domain, this equation
possesses plane wave solutions that are explicit. We prove that these solutions
are asymptotically stable in Sobolev regularity. In the case without damping,
we prove that for almost all value of the nonlinear parameter, these solutions
are stable in high Sobolev regularity for arbitrary long times when the
solution is close to a plane wave. We also show and discuss numerical
experiments illustrating our results.
|
2111.01487v1
|
2021-11-11
|
Stabilization for Euler-Bernoulli beam equation with a local degenerated Kelvin-Voigt damping
|
We consider the Euler-Bernoulli beam equation with a local Kelvin-Voigt
dissipation type in the interval $(-1,1)$. The coefficient damping is only
effective in $(0,1)$ and is degenerating near the $0$ point with a speed at
least equal to $x^{\alpha}$ where $\alpha\in(0,5)$. We prove that the semigroup
corresponding to the system is polynomially stable and the decay rate depends
on the degeneracy speed $\alpha$.
|
2111.06431v1
|
2021-11-12
|
GCGE: A Package for Solving Large Scale Eigenvalue Problems by Parallel Block Damping Inverse Power Method
|
We propose an eigensolver and the corresponding package, GCGE, for solving
large scale eigenvalue problems. This method is the combination of damping
idea, subspace projection method and inverse power method with dynamic shifts.
To reduce the dimensions of projection subspaces, a moving mechanism is
developed when the number of desired eigenpairs is large. The numerical
methods, implementing techniques and the structure of the package are
presented. Plenty of numerical results are provided to demonstrate the
efficiency, stability and scalability of the concerned eigensolver and the
package GCGE for computing many eigenpairs of large symmetric matrices arising
from applications.
|
2111.06552v1
|
2021-11-25
|
Continuity and topological structural stability for nonautonomous random attractors
|
In this work, we study continuity and topological structural stability of
attractors for nonautonomous random differential equations obtained by small
bounded random perturbations of autonomous semilinear problems. First, we study
existence and permanence of unstable sets of hyperbolic solutions. Then, we use
this to establish lower semicontinuity of nonautonomous random attractors and
to show that the gradient structure persists under nonautonomous random
perturbations. Finally, we apply the abstract results in a stochastic
differential equation and in a damped wave equation with a perturbation on the
damping.
|
2111.13006v1
|
2021-11-30
|
Determining damping terms in fractional wave equations
|
This paper deals with the inverse problem of recovering an arbitrary number
of fractional damping terms in a wave equation. We develop several approaches
on uniqueness and reconstruction, some of them relying on Tauberian theorems on
the relation between the asymptotics of solutions in time and Laplace domain.
Also the possibility of additionally recovering space dependent coefficients or
initial data is discussed. The resulting methods for reconstructing
coefficients and fractional orders in these terms are tested numerically.
Additionally, we provide an analysis of the forward problem, a multiterm
fractional wave equation.
|
2112.00080v2
|
2021-12-20
|
Dense Coding Capacity in Correlated Noisy Channels with Weak Measurement
|
Capacity of dense coding via correlated noisy channel is greater than that in
uncorrelated noisy channel. It is shown that weak measurement and reversal
measurement can make further effort to improve quantum dense coding capacity in
correlated amplitude damping channel, but this effort is very small in
correlated phase damping channel and correlated depolarizing channel.
|
2112.10346v1
|
2021-12-22
|
Low-frequency squeezing spectrum of a laser drivenpolar quantum emitter
|
It was shown by a study of the incoherent part of the low-frequency resonance
fluorescence spectrum of the polar quantum emitter driven by semiclassical
external laser field and damped by non-squeezed vacuum reservoir that the
emitted fluorescence field is squeezed to some degree nevertheless. As was also
found, a higher degree of squeezing could, in principle, be achieved by damping
the emitter by squeezed vacuum reservoir.
|
2112.11809v1
|
2022-01-13
|
Cavity optomechanics in a fiber cavity: the role of stimulated Brillouin scattering
|
We study the role of stimulated Brillouin scattering in a fiber cavity by
numerical simulations and a simple theoretical model and find good agreement
between experiment, simulation and theory. We also investigate an
optomechanical system based on a fiber cavity in the presence on the nonlinear
Brillouin scattering. Using simulation and theory, we show that this hybrid
optomechanical system increases optomechanical damping for low mechanical
resonance frequencies in the unresolved sideband regime. Furthermore, optimal
damping occurs for blue detuning in stark contrast to standard optomechanics.
We investigate whether this hybrid optomechanical system is capable cooling a
mechanical oscillator to the quantum ground state.
|
2201.04987v1
|
2022-01-20
|
Vacuum and singularity formation for compressible Euler equations with time-dependent damping
|
In this paper, vacuum and singularity formation are considered for
compressible Euler equations with time-dependent damping. For $1<\gamma\leq 3$,
by constructing some new control functions ingeniously, we obtain the lower
bounds estimates on density for arbitrary classical solutions. Basing on these
lower estimates, we succeed in proving the singular formation theorem for all
$\lambda$, which was open in [1] for some cases.Moreover, the singularity
formation of the compressible Euler equations when $\gamma=3$ is investigated,
too.
|
2201.07957v1
|
2022-01-22
|
Absorption of charged particles in Perfectly-Matched-Layers by optimal damping of the deposited current
|
Perfectly-Matched Layers (PML) are widely used in Particle-In-Cell
simulations, in order to absorb electromagnetic waves that propagate out of the
simulation domain. However, when charged particles cross the interface between
the simulation domain and the PMLs, a number of numerical artifacts can arise.
In order to mitigate these artifacts, we introduce a new PML algorithm whereby
the current deposited by the macroparticles in the PML is damped by an
analytically-derived, optimal coefficient. The benefits of this new algorithm
is illustrated in practical simulations.
|
2201.09084v2
|
2022-03-19
|
The Equilibrium Temperature of Planets on Eccentric Orbits: Time Scales and Averages
|
From estimates of the near-surface heat capacity of planets it is shown that
the thermal time scale is larger than the orbital period in the presence of a
global ocean that is well-mixed to a depth of 100 m, or of an atmosphere with a
pressure of several tens of bars. As a consequence, the temperature
fluctuations of such planets on eccentric orbits are damped. The average
temperature should be calculated by taking the temporal mean of the irradiation
over an orbit, which increases with $1/\sqrt{1-e^2}$. This conclusion is
independent of the orbital distance and valid for Sun-like stars; the damping
is even stronger for low-mass main sequence hosts.
|
2203.11723v1
|
2022-03-31
|
Long-time dynamical behavior for a piezoelectric system with magnetic effect and nonlinear dampings
|
This paper is concerned with the long-time dynamical behavior of a
piezoelectric system with magnetic effect, which has nonlinear damping terms
and external forces with a parameter. At first, we use the nonlinear semigroup
theory to prove the well-posedness of solutions. Then, we investigate the
properties of global attractors and the existence of exponential attractors.
Finally, the upper semicontinuity of global attractors has been investigated.
|
2203.16736v1
|
2022-04-04
|
Exponential ergodicity for damping Hamiltonian dynamics with state-dependent and non-local collisions
|
In this paper, we investigate the exponential ergodicity in a
Wasserstein-type distance for a damping Hamiltonian dynamics with
state-dependent and non-local collisions, which indeed is a special case of
piecewise deterministic Markov processes while is very popular in numerous
modelling situations including stochastic algorithms. The approach adopted in
this work is based on a combination of the refined basic coupling and the
refined reflection coupling for non-local operators. In a certain sense, the
main result developed in the present paper is a continuation of the counterpart
in \cite{BW2022} on exponential ergodicity of stochastic Hamiltonian systems
with L\'evy noises and a complement of \cite{BA} upon exponential ergodicity
for Andersen dynamics with constant jump rate functions.
|
2204.01372v1
|
2022-04-08
|
Effect of Tamm surface states on hot electron generation and Landau damping in nanostructures metal-semiconductor
|
The hot electron generation in plasmonic nanoparticles is the key to
efficient plasmonic photocatalysis. In the paper, we study theoretically for
the first time the effect of Tamm states (TSs) at the interface
metal-semiconductor on hot electron generation and Landau damping (LD) in metal
nanoparticles. TSs can lead to resonant hot electron generation and to the LD
rate enhanced by several times. The resonant hot electron generation is
reinforced by the transition absorption due to the jump of the permittivity at
the metal-semiconductor interface.
|
2204.04021v1
|
2022-04-11
|
Certified Reduced Basis Method for the Damped Wave Equations on Networks
|
In this paper we present a reduced basis method which yields
structure-preservation and a tight a posteriori error bound for the simulation
of the damped wave equations on networks. The error bound is based on the
exponential decay of the energy inside the system and therefore allows for
sharp bounds without the need of regularization parameters. The fast
convergence of the reduced solution to the truth solution as well as the
tightness of the error bound are verified numerically using an academic network
as example.
|
2204.05010v1
|
2022-04-27
|
Spectrum of the wave equation with Dirac damping on a non-compact star graph
|
We consider the wave equation on non-compact star graphs, subject to a
distributional damping defined through a Robin-type vertex condition with
complex coupling. It is shown that the non-self-adjoint generator of the
evolution problem admits an abrupt change in its spectral properties for a
special coupling related to the number of graph edges. As an application, we
show that the evolution problem is highly unstable for the critical couplings.
The relationship with the Dirac equation in non-relativistic quantum mechanics
is also mentioned.
|
2204.12747v1
|
2022-04-27
|
Dependence on the thermodynamic state of self-diffusion of pseudo hard-spheres
|
Self-diffusion, $D$, in a system of particles that interact with a pseudo
hard sphere potential is analyzed. Coupling with a solvent is represented by a
Langevin thermostat, characterized by the damping time $t_d$. The hypotheses
that $D=D_0 \varphi$ is proposed, where $D_0$ is the small concentration
diffusivity and $\varphi$ is a thermodynamic function that represents the
effects of interactions as concentration is increased. Molecular dynamics
simulations show that different values of the noise intensity modify $D_0$ but
do not modify $\varphi$. This result is consistent with the assumption that
$\varphi$ is a thermodynamic function, since the thermodynamic state is not
modified by the presence of damping and noise.
|
2204.12969v1
|
2022-04-29
|
Plasmon damping rates in Coulomb-coupled two-dimensional layers in a heterostructure
|
The Coulomb excitations of charge density oscillation are calculated for a
double-layer heterostructure. Specifically, we consider two-dimensional (2D)
layers of silicene and graphene on a substrate. From the obtained surface
response function, we calculated the plasmon dispersion relations which
demonstrate the way in which the Coulomb coupling renormalizes the plasmon
frequencies. Additionally, we present a novel result for the damping rates of
the plasmons in this Coulomb coupled heterostructure and compare these results
as the separation between layers is varied.
|
2205.00053v1
|
2022-05-08
|
A regularity criterion for a 3D tropical climate model with damping
|
In this paper we deal with the 3D tropical climate model with damping terms
in the equation of the barotropic mode $u$ and in the equation of the first
baroclinic mode $v$ of the velocity, and we establish a regularity criterion
for this system thanks to which the local smooth solution $(u, v, \theta)$ can
actually be extended globally in time.
|
2205.03841v3
|
2022-06-04
|
Radiation backreaction in axion electrodynamics
|
Energy-momentum conservation of classical axion-electrodynamics is carefully
analyzed in the Hamiltonian formulation of the theory. The term responsible for
the energy transfer between the electromagnetic and the axion sectors is
identified. As a special application the axion-to-light Primakoff-process in
the background of a static magnetic field is worked out and the radiative
self-damping of the axion oscillations is characterized quantitatively. The
damping time turns out comparable to the age of the Universe in the preferred
axion mass range.
|
2206.02052v1
|
2022-06-07
|
Strong attractors for weakly damped quintic wave equation in bounded domains
|
In this paper, we study the longtime dynamics for the weakly damped wave
equation with quintic non-linearity in a bounded smooth domain of
$\mathbb{R}^3.$ Based on the Strichartz estimates for the case of bounded
domains, we establish the existence of a strong global attractor in the phase
space $H^2(\Omega)\cap H^1_0(\Omega)\times H^1_0(\Omega)$. Moreover, the finite
fractal dimension of the attractor is also shown with the help of the
quasi-stable estimation.
|
2206.03158v1
|
2022-06-07
|
Long-time dynamics of the wave equation with nonlocal weak damping and sup-cubic nonlinearity in 3-D domains
|
In this paper, we study the long-time dynamics for the wave equation with
nonlocal weak damping and sup-cubic nonlinearity in a bounded smooth domain of
$\mathbb{R}^3.$ Based on the Strichartz estimates for the case of bounded
domains, we first prove the global well-posedness of the Shatah-Struwe
solutions. Then we establish the existence of the global attractor for the
Shatah-Struwe solution semigroup by the method of contractive function.
Finally, we verify the existence of a polynomial attractor for this semigroup.
|
2206.03163v1
|
2022-06-17
|
On energy-stable and high order finite element methods for the wave equation in heterogeneous media with perfectly matched layers
|
This paper presents a stable finite element approximation for the acoustic
wave equation on second-order form, with perfectly matched layers (PML) at the
boundaries. Energy estimates are derived for varying PML damping for both the
discrete and the continuous case. Moreover, a priori error estimates are
derived for constant PML damping. Most of the analysis is performed in Laplace
space. Numerical experiments in physical space validate the theoretical
results.
|
2206.08507v1
|
2022-06-20
|
Harmonic Oscillators of Mathematical Biology: Many Faces of a Predator-Prey Model
|
We show that a number of models in virus dynamics, epidemiology and plant
biology can be presented as ``damped" versions of the Lotka-Volterra
predator-prey model, by analogy to the damped harmonic oscillator. The analogy
deepens with the use of Lyapunov functions, which allow us to characterize
their dynamics and even make some estimates.
|
2206.09561v1
|
2022-06-21
|
Phase-covariant mixtures of non-unital qubit maps
|
We analyze convex combinations of non-unital qubit maps that are
phase-covariant. In particular, we consider the behavior of maps that combine
amplitude damping, inverse amplitude damping, and pure dephasing. We show that
mixing non-unital channels can result in restoring the unitality, whereas
mixing commutative maps can lead to non-commutativity. For the convex
combinations of Markovian semigroups, we prove that classical uncertainties
cannot break quantum Markovianity. Moreover, contrary to the Pauli channel
case, the semigroup can be recovered only by mixing two other semigroups.
|
2206.10742v1
|
2022-07-01
|
Stabilization results of a Lorenz piezoelectric beam with partial viscous dampings
|
In this paper, we investigate the stabilization of a one-dimensional Lorenz
piezoelectric (Stretching system) with partial viscous dampings. First, by
using Lorenz gauge conditions, we reformulate our system to achieve the
existence and uniqueness of the solution. Next, by using General criteria of
Arendt-Batty, we prove the strong stability in different cases. Finally, we
prove that it is sufficient to control the stretching of the center-line of the
beam in x-direction to achieve the exponential stability. Numerical results are
also presented to validate our theoretical result.
|
2207.00488v1
|
2022-07-06
|
Quantum Decomposition Algorithm For Master Equations of Stochastic Processes: The Damped Spin Case
|
We introduce a quantum decomposition algorithm (QDA) that decomposes the
problem $\frac{\partial \rho}{\partial t}=\mathcal{L}\rho=\lambda \rho$ into a
summation of eigenvalues times phase-space variables. One interesting feature
of QDA stems from its ability to simulate damped spin systems by means of pure
quantum harmonic oscillators adjusted with the eigenvalues of the original
eigenvalue problem. We test the proposed algorithm in the case of undriven
qubit with spontaneous emission and dephasing.
|
2207.02755v3
|
2022-07-25
|
Geometric modelling of polycrystalline materials: Laguerre tessellations and periodic semi-discrete optimal transport
|
In this paper we describe a fast algorithm for generating periodic RVEs of
polycrystalline materials. In particular, we use the damped Newton method from
semi-discrete optimal transport theory to generate 3D periodic Laguerre
tessellations (or power diagrams) with cells of given volumes. Complex,
polydisperse RVEs with up to 100,000 grains of prescribed volumes can be
created in a few minutes on a standard laptop. The damped Newton method relies
on the Hessian of the objective function, which we derive by extending recent
results in semi-discrete optimal transport theory to the periodic setting.
|
2207.12036v1
|
2022-07-27
|
Subsonic time-periodic solution to compressible Euler equations with damping in a bounded domain
|
In this paper, we consider the one-dimensional isentropic compressible Euler
equations with linear damping $\beta(t,x)\rho u$ in a bounded domain, which can
be used to describe the process of compressible flows through a porous
medium.~And the model is imposed a dissipative subsonic time-periodic boundary
condition.~Our main results reveal that the time-periodic boundary can trigger
a unique subsonic time-periodic smooth solution which is stable under small
perturbations on initial data. Moreover, the time-periodic solution possesses
higher regularity and stability provided a higher regular boundary condition.
|
2207.13433v1
|
2022-09-10
|
Landau damping on the torus for the Vlasov-Poisson system with massless electrons
|
This paper studies the nonlinear Landau damping on the torus $\mathbb{T}^d$
for the Vlasov-Poisson system with massless electrons (VPME). We consider
solutions with analytic or Gevrey ($\gamma > 1/3$) initial data, close to a
homogeneous equilibrium satisfying a Penrose stability condition. We show that
for such solutions, the corresponding density and force field decay
exponentially fast as time goes to infinity. This work extends the results for
Vlasov-Poisson on the torus to the case of ions and, more generally, to
arbitrary analytic nonlinear couplings.
|
2209.04676v2
|
2022-09-25
|
Polynomial mixing of a stochastic wave equation with dissipative damping
|
We study the long time statistics of a class of semi--linear wave equations
modeling the motions of a particle suspended in continuous media while being
subjected to random perturbations via an additive Gaussian noise. By comparison
with the nonlinear reaction settings, of which the solutions are known to
possess geometric ergodicity, we find that, under the impact of nonlinear
dissipative damping, the mixing rate is at least polynomial of any order. This
relies on a combination of Lyapunov conditions, the contracting property of the
Markov transition semigroup as well as the notion of $d$--small sets.
|
2209.12151v2
|
2022-09-30
|
A Lyapunov approach for the exponential stability of a damped Timoshenko beam
|
In this technical note, we consider the stability properties of a viscously
damped Timoshenko beam equation with spatially varying parameters. With the
help of the port-Hamiltonian framework, we first prove the existence of
solutions and show, by an appropriate Lyapunov function, that the system is
exponentially stable and has an explicit decay rate. The explicit exponential
bound is computed for an illustrative example of which we provide some
numerical simulations.
|
2209.15281v1
|
2022-11-01
|
Well-posedness and strong attractors for a beam model with degenerate nonlocal strong damping
|
This paper is devoted to initial-boundary value problem of an extensible beam
equation with degenerate nonlocal energy damping in
$\Omega\subset\mathbb{R}^n$: $u_{tt}-\kappa\Delta u+\Delta^2u-\gamma(\Vert
\Delta u\Vert^2+\Vert u_t\Vert^2)^q\Delta u_t+f(u)=0$. We prove the global
existence and uniqueness of weak solutions, which gives a positive answer to an
open question in [24]. Moreover, we establish the existence of a strong
attractor for the corresponding weak solution semigroup, where the ``strong"
means that the compactness and attractiveness of the attractor are in the
topology of a stronger space $\mathcal{H}_{\frac{1}{q}}$.
|
2211.00287v3
|
2022-11-18
|
Energy decay estimates for an axially travelling string damped at one end
|
We study the small vibrations of an axially travelling string with a
dashpoint damping at one end. The string is modelled by a wave equation in a
time-dependent interval with two endpoints moving at a constant speed $v$. For
the undamped case, we obtain a conserved functional equivalent to the energy of
the solution. We derive precise upper and lower estimates for the exponential
decay of the energy with explicit constants. These estimates do not seem to be
reported in the literature even for the non-travelling case $v=0$.
|
2211.10537v1
|
2022-12-01
|
The viscous damping of three dimensional spherical gas bubble inside unbounded compressible liquid
|
The present paper considers a homogeneous bubble inside an unbounded
polytropic compressible liquid with viscosity. The system is governed by the
Navier-Stokes equation with free boundary which is determined by the kinematic
and dynamic boundary conditions on the bubble-liquid interface. The global
existence of solution is proved, and the $\dot{H}^1$ asymptotic stability of
the spherical equilibrium in terms of viscous damping together with a explicit
decay rate is given in bare energy methods.
|
2212.00299v1
|
2022-12-27
|
Stabilization of the Kawahara-Kadomtsev-Petviashvili equation with time-delayed feedback
|
Results of stabilization for the higher order of the Kadomtsev-Petviashvili
equation are presented in this manuscript. Precisely, we prove with two
different approaches that under the presence of a damping mechanism and an
internal delay term (anti-damping) the solutions of the
Kawahara-Kadomtsev-Petviashvili equation are locally and globally exponentially
stable. The main novelty is that we present the optimal constant, as well as
the minimal time, that ensures that the energy associated with this system goes
to zero exponentially.
|
2212.13552v1
|
2023-02-23
|
Hopf-Like Bifurcation in a Wave Equation at a Removable Singularity
|
It is shown that a one-dimensional damped wave equation with an odd time
derivative nonlinearity exhibits small amplitude bifurcating time periodic
solutions, when the bifurcation parameter is the linear damping coefficient is
positive and accumulates to zero. The upshot is that the singularity of the
linearized operator at criticality which stems from the well known small
divisor problem for the wave operator, is entirely removed without the need to
exclude parameters via Diophantine conditions, nor the use of accelerated
convergence schemes. Only the contraction mapping principle is used.
|
2302.12092v2
|
2023-03-11
|
Control estimates for 0th order pseudodifferential operators
|
We introduce the control conditions for 0th order pseudodifferential
operators $\mathbf{P}$ whose real parts satisfy the Morse--Smale dynamical
condition. We obtain microlocal control estimates under the control conditions.
As a result, we show that there are no singular profiles in the solution to the
evolution equation $(i\partial_t-\mathbf{P})u=f$ when $\mathbf{P}$ has a
damping term that satisfies the control condition and $f\in C^{\infty}$. This
is motivated by the study of a microlocal model for the damped internal waves.
|
2303.06443v2
|
2023-03-24
|
Exponential decay estimates for semilinear wave-type equations with time-dependent time delay
|
In this paper, we analyze a semilinear damped second order evolution equation
with time-dependent time delay and time-dependent delay feedback coefficient.
The nonlinear term satisfies a local Lipschitz continuity assumption. Under
appropriate conditions, we prove well-posedness and exponential stability of
our model for small initial data. Our arguments combine a Lyapunov functional
approach with some continuity arguments. Moreover, as an application of our
abstract results, the damped wave equation with a source term and delay
feedback is analyzed.
|
2303.14208v1
|
2023-03-25
|
Existence and regularity of global attractors for a Kirchhoff wave equation with strong damping and memory
|
This paper is concerned with the existence and regularity of global attractor
$\mathcal A$ for a Kirchhoff wave equation with strong damping and memory in
the weighted time-dependent spaces $\mathcal H$ and $\mathcal H^{1}$,
respectively. In order to obtain the existence of $\mathcal A$, we mainly use
the energy method in the priori estimations, and then verify the asymptotic
compactness of the semigroup by the method of contraction function. Finally, by
decomposing the weak solutions into two parts and some elaborate calculations,
we prove the regularity of $\mathcal A$.
|
2303.14387v1
|
2023-03-27
|
Linear Landau damping for a two-species Vlasov-Poisson system for electrons and ions
|
This paper concerns the linear Landau damping for the two species
Vlasov-Poisson system for ions and electrons near Penrose stable equilibria.
The result is an extension of the result on the one species Vlasov-Poisson
equation by Mouhout and Villani. Different from their work we do not describe
the ions as a background species but as a species which is also described by a
separate Vlasov equation. We show an exponential decay of the electric energy
for the linearised system near Penrose stable equilibria.
|
2303.14981v2
|
2023-03-28
|
Role of intersublattice exchange interaction on ultrafast longitudinal and transverse magnetization dynamics in Permalloy
|
We report about element specific measurements of ultrafast demagnetization
and magnetization precession damping in Permalloy (Py) thin films.
Magnetization dynamics induced by optical pump at $1.5$eV is probed
simultaneously at the $M_{2,3}$ edges of Ni and Fe with High order Harmonics
for moderate demagnetization rates (less than $50$%). The role of the
intersublattice exchange interaction on both longitudinal and transverse
dynamics is analyzed with a Landau Lifshitz Bloch description of
ferromagnetically coupled Fe and Ni sublattices. It is shown that the
intersublattice exchange interaction governs the dissipation during
demagnetization as well as precession damping of the magnetization vector.
|
2303.15837v1
|
2023-03-31
|
Polynomial Mixing for a Weakly Damped Stochastic Nonlinear Schrödinger Equation
|
This paper is devoted to proving the polynomial mixing for a weakly damped
stochastic nonlinear Schr\"{o}dinger equation with additive noise on a 1D
bounded domain. The noise is white in time and smooth in space. We consider
both focusing and defocusing nonlinearities, respectively, with exponents of
the nonlinearity $\sigma\in[0,2)$ and $\sigma\in[0,\infty)$ and prove the
polynomial mixing which implies the uniqueness of the invariant measure by
using a coupling method.
|
2303.18082v1
|
2023-04-19
|
Inviscid damping of monotone shear flows for 2D inhomogeneous Euler equation with non-constant density in a finite channel
|
We prove the nonlinear inviscid damping for a class of monotone shear flows
with non-constant background density for the two-dimensional ideal
inhomogeneous fluids in $\mathbb{T}\times [0,1]$ when the initial perturbation
is in Gevrey-$\frac{1}{s}$ ($\frac{1}{2}<s<1$) class with compact support.
|
2304.09841v2
|
2023-05-07
|
Nonexistence of global weak solutions to semilinear wave equations involving time-dependent structural damping terms
|
We consider a semilinear wave equation involving a time-dependent structural
damping term of the form
$\displaystyle\frac{1}{{(1+t)}^{\beta}}(-\Delta)^{\sigma/2} u_t$. Our results
show the influence of the parameters $\beta,\sigma$ on the nonexistence of
global weak solutions under assumptions on the given system data.
|
2305.04278v1
|
2023-05-15
|
Blow-up phenomena for a class of extensible beam equations
|
In this paper, we investigate the initial boundary value problem of the
following nonlinear extensible beam equation with nonlinear damping term $$u_{t
t}+\Delta^2 u-M\left(\|\nabla u\|^2\right) \Delta u-\Delta
u_t+\left|u_t\right|^{r-1} u_t=|u|^{p-1} u$$ which was considered by Yang et
al. (Advanced Nonlinear Studies 2022; 22:436-468). We consider the problem with
the nonlinear damping and establish the finite time blow-up of the solution for
the initial data at arbitrary high energy level, including the estimate lower
and upper bounds of the blowup time. The result provides some affirmative
answer to the open problems given in (Advanced Nonlinear Studies 2022;
22:436-468).
|
2305.08398v1
|
2023-06-08
|
Vanishing of long time average p-enstrophy dissipation rate in the inviscid limit of the 2D damped Navier-Stokes equations
|
In 2007, Constantin and Ramos proved a result on the vanishing long time
average enstrophy dissipation rate in the inviscid limit of the 2D damped
Navier-Stokes equations. In this work, we prove a generalization of this for
the p-enstrophy, sequences of distributions of initial data and sequences of
strongly converging right-hand sides. We simplify their approach by working
with invariant measures on the global attractors which can be characterized via
bounded complete solution trajectories. Then, working on the level of
trajectories allows us to directly employ some recent results on strong
convergence of the vorticity in the inviscid limit.
|
2306.05081v1
|
2023-06-13
|
Stability of asymptotically Hamiltonian systems with damped oscillatory and stochastic perturbations
|
A class of asymptotically autonomous systems on the plane with oscillatory
coefficients is considered. It is assumed that the limiting system is
Hamiltonian with a stable equilibrium. The effect of damped multiplicative
stochastic perturbations of white noise type on the stability of the system is
discussed. It is shown that different long-term asymptotic regimes for
solutions are admissible in the system and the stochastic stability of the
equilibrium depends on the realized regime. In particular, we show that stable
phase locking is possible in the system due to decaying stochastic
perturbations. The proposed analysis is based on a combination of the averaging
technique and the construction of stochastic Lyapunov functions.
|
2306.07694v1
|
2023-06-16
|
Algorithm MGB to solve highly nonlinear elliptic PDEs in $\tilde{O}(n)$ FLOPS
|
We introduce Algorithm MGB (Multi Grid Barrier) for solving highly nonlinear
convex Euler-Lagrange equations. This class of problems includes many highly
nonlinear partial differential equations, such as $p$-Laplacians. We prove
that, if certain regularity hypotheses are satisfied, then our algorithm
converges in $\tilde{O}(1)$ damped Newton iterations, or $\tilde{O}(n)$ FLOPS,
where the tilde indicates that we neglect some polylogarithmic terms. This the
first algorithm whose running time is proven optimal in the big-$\tilde{O}$
sense. Previous algorithms for the $p$-Laplacian required $\tilde{O}(\sqrt{n})$
damped Newton iterations or more.
|
2306.10183v1
|
2023-06-28
|
Global solutions and blow-up for the wave equation with variable coefficients: II. boundary supercritical source
|
In this paper, we consider the wave equation with variable coefficients and
boundary damping and supercritical source terms. The goal of this work is
devoted to prove the local and global existence, and classify decay rate of
energy depending on the growth near zero on the damping term. Moreover, we
prove the blow-up of the weak solution with positive initial energy as well as
nonpositive initial energy.
|
2306.15897v4
|
2023-07-24
|
On the stability of a double porous elastic system with visco-porous dampings
|
In this paper we consider a one dimensional elastic system with double
porosity structure and with frictional damping in both porous equations. We
introduce two stability numbers $\chi_{0}$ and $\chi_{1}$ and prove that the
solution of the system decays exponentially provided that $\chi_{0}=0$ and
$\chi_{1}\neq0.$ Otherwise, we prove the lack of exponential decay. Our results
improve the results of \cite{Bazarra} and \cite{Nemsi}.
|
2307.12690v1
|
2023-07-27
|
Best Ulam constants for damped linear oscillators with variable coefficients
|
This study uses an associated Riccati equation to study the Ulam stability of
non-autonomous linear differential vector equations that model the damped
linear oscillator. In particular, the best (minimal) Ulam constants for these
non-autonomous linear differential vector equations are derived. These robust
results apply to vector equations with solutions that blow up in finite time,
as well as to vector equations with solutions that exist globally on
$(-\infty,\infty)$. Illustrative, non-trivial examples are presented,
highlighting the main results.
|
2307.15103v1
|
2023-07-29
|
An inverse problem for the fractionally damped wave equation
|
We consider an inverse problem for a Westervelt type nonlinear wave equation
with fractional damping. This equation arises in nonlinear acoustic imaging,
and we show the forward problem is locally well-posed. We prove that the smooth
coefficient of the nonlinearity can be uniquely determined, based on the
knowledge of the source-to-solution map and a priori knowledge of the
coefficient in an arbitrarily small subset of the domain. Our approach relies
on a second order linearization as well as the unique continuation property of
the spectral fractional Laplacian.
|
2307.16065v1
|
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