publicationDate
stringlengths
1
2.79k
title
stringlengths
1
36.5k
abstract
stringlengths
1
37.3k
id
stringlengths
9
47
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 e...
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 ...
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 wel...
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 th...
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 glo...
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 ...
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 t...
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 c...
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 $...
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 stud...
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 en...
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 prob...
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, namel...
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 infin...
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...
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 ...
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 kn...
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 perio...
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...
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. Fi...
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 b...
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...
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 th...
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 non...
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...
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...
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 amp...
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 multiplie...
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 s...
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 d...
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 ...
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 s...
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 showi...
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 ...
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 ...
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 r...
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 mu...
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 s...
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 classica...
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 matri...
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, ...
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~...
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 capabili...
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 ...
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 o...
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 te...
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 th...
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 ...
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 ...
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 e...
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...
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...
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 high...
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. Us...
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, w...
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 mit...
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 s...
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 at...
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...
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...
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 o...
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...
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 $...
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...
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 ...
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 backgroun...
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(...
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 est...
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 con...
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...
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 ...
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 pro...
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 har...
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...
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.~Ou...
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 soluti...
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 geome...
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...
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 solutio...
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. W...
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 solutio...
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 ...
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 operat...
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 equati...
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 f...
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...
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...
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 rate...
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 $...
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 ...
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...
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 show...
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 $\til...
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 o...
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 $\chi_{1}\neq0.$ Othe...
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 appl...
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 ...
2307.16065v1