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2015-03-14 | Stabilization of the nonlinear damped wave equation via linear weak observability | We consider the problem of energy decay rates for nonlinearly damped abstract
infinite dimensional systems. We prove sharp, simple and quasi-optimal energy
decay rates through an indirect method, namely a weak observability estimate
for the corresponding undamped system. One of the main advantage of these
results is th... | 1503.04356v1 |
2015-04-23 | Magnetization damping in noncollinear spin valves with antiferromagnetic interlayer couplings | We study the magnetic damping in the simplest of synthetic antiferromagnets,
i.e. antiferromagnetically exchange-coupled spin valves in which applied
magnetic fields tune the magnetic configuration to become noncollinear. We
formulate the dynamic exchange of spin currents in a noncollinear texture based
on the spindiff... | 1504.06042v1 |
2015-06-02 | On the the wave equation with hyperbolic dynamical boundary conditions, interior and boundary damping and source | The aim of the paper is to study local Hadamard well-posedness for wave
equation with an hyperbolic dynamical boundary condition, internal and/or
boundary damping and sources for initial data in the natural energy space.
Moreover the regularity of solutions is studied. Finally a dynamical system is
generated when sourc... | 1506.00910v4 |
2015-06-15 | Tautochrone in the damped cycloidal pendulum | The tautochrone on a cycloid curve is usually considered without drag force.
In this work, we investigate the motion of a damped cycloidal pendulum under
presence of a drag force. Using the Lagrange formulation, and considering
linear dependence with velocity for damping force, we found the dynamics of the
system to re... | 1506.04943v2 |
2015-07-04 | Comments on turbulence theory by Qian and by Edwards and McComb | We reexamine Liouville equation based turbulence theories proposed by Qian
{[}Phys. Fluids \textbf{26}, 2098 (1983){]} and Edwards and McComb {[}J. Phys.
A: Math. Gen. \textbf{2}, 157 (1969){]}, which are compatible with Kolmogorov
spectrum. These theories obtained identical equation for spectral density
$q(k)$ and dif... | 1507.01124v1 |
2015-08-24 | Scaling variables and asymptotic profiles for the semilinear damped wave equation with variable coefficients | We study the asymptotic behavior of solutions for the semilinear damped wave
equation with variable coefficients. We prove that if the damping is effective,
and the nonlinearity and other lower order terms can be regarded as
perturbations, then the solution is approximated by the scaled Gaussian of the
corresponding li... | 1508.05778v3 |
2015-10-01 | Impact of surface collisions on enhancement and quenching of the luminescence near the metal nanoparticles | The fact that surface-induced damping rate of surface plasmon polaritons
(SPPs) in metal nanoparticles increases with the decrease of particle size is
well known. We show that this rate also increases with the degree of the mode
confinement, hence damping of the higher order nonradiative SPP modes in
spherical particle... | 1510.00321v1 |
2015-10-22 | On numerical Landau damping for splitting methods applied to the Vlasov-HMF model | We consider time discretizations of the Vlasov-HMF (Hamiltonian Mean-Field)
equation based on splitting methods between the linear and non-linear parts. We
consider solutions starting in a small Sobolev neighborhood of a spatially
homogeneous state satisfying a linearized stability criterion (Penrose
criterion). We pro... | 1510.06555v1 |
2015-11-02 | Asymptotic decomposition for nonlinear damped Klein-Gordon equations | In this paper, we proved that if the solution to damped focusing Klein-Gordon
equations is global forward in time, then it will decouple into a finite number
of equilibrium points with different shifts from the origin. The core
ingredient of our proof is the existence of the "concentration-compact
attractor" which yiel... | 1511.00437v3 |
2015-11-11 | Contact Stiffness and Damping of Liquid Films in Dynamic Atomic Force Microscopy | Small-amplitude dynamic atomic force microscopy (dynamic-AFM) in a simple
nonpolar liquid was studied through molecular dynamics simulations. We find
that within linear dynamics regime, the contact stiffness and damping of the
confined film exhibit the similar solvation force oscillations, and they are
generally out-of... | 1511.03580v1 |
2015-11-13 | Nonlinear Radiation Damping of Nuclear Spin Waves and Magnetoelastic Waves in Antiferromagnets | Parallel pumping of nuclear spin waves in antiferromagnetic CsMnF3 at liquid
helium temperatures and magnetoelastic waves in antiferromagnetic FeBO3 at
liquid nitrogen temperature in a helical resonator was studied. It was found
that the absorbed microwave power is approximately equal to the irradiated
power from the s... | 1511.04396v1 |
2016-03-01 | Damped vacuum states of light | We consider one-dimensional propagation of quantum light in the presence of a
block of material, with a full account of dispersion and absorption. The
electromagnetic zero-point energy for some frequencies is damped (suppressed)
by the block below the free-space value, while for other frequencies it is
increased. We al... | 1603.00233v2 |
2016-04-20 | Landau damping in finite regularity for unconfined systems with screened interactions | We prove Landau damping for the collisionless Vlasov equation with a class of
$L^1$ interaction potentials (including the physical case of screened Coulomb
interactions) on $\mathbb R^3_x \times \mathbb R^3_v$ for localized
disturbances of an infinite, homogeneous background. Unlike the confined case
$\mathbb T^3_x \ti... | 1604.05783v1 |
2016-04-26 | Trigonometric Splines for Oscillator Simulation | We investigate the effects of numerical damping for oscillator simulation
with spline methods. Numerical damping results in an artificial loss of energy
and leads therefore to unreliable results in the simulation of autonomous
systems, as e.g.\ oscillators. We show that the negative effects of numerical
damping can be ... | 1604.07607v1 |
2016-05-05 | Theory of magnon motive force in chiral ferromagnets | We predict that magnon motive force can lead to temperature dependent,
nonlinear chiral damping in both conducting and insulating ferromagnets. We
estimate that this damping can significantly influence the motion of skyrmions
and domain walls at finite temperatures. We also find that in systems with low
Gilbert damping... | 1605.01694v2 |
2016-08-29 | Stochastic 3D Navier-Stokes equations with nonlinear damping: martingale solution, strong solution and small time large deviation principles | In this paper, by using classical Faedo-Galerkin approximation and
compactness method, the existence of martingale solutions for the stochastic 3D
Navier-Stokes equations with nonlinear damping is obtained. The existence and
uniqueness of strong solution are proved for $\beta > 3$ with any $\alpha>0$
and $\alpha \geq \... | 1608.07996v1 |
2016-09-05 | Estimates of lifespan and blow-up rates for the wave equation with a time-dependent damping and a power-type nonlinearity | We study blow-up behavior of solutions for the Cauchy problem of the
semilinear wave equation with time-dependent damping. When the damping is
effective, and the nonlinearity is subcritical, we show the blow-up rates and
the sharp lifespan estimates of solutions. Upper estimates are proved by an ODE
argument, and lower... | 1609.01035v2 |
2016-09-06 | Numerical Convergence Rate for a Diffusive Limit of Hyperbolic Systems: p-System with Damping | This paper deals with diffusive limit of the p-system with damping and its
approximation by an Asymptotic Preserving (AP) Finite Volume scheme. Provided
the system is endowed with an entropy-entropy flux pair, we give the
convergence rate of classical solutions of the p-system with damping towards
the smooth solutions ... | 1609.01436v1 |
2016-11-08 | Emulated Inertia and Damping of Converter-Interfaced Power Source | Converter-interfaced power sources (CIPSs), like wind turbine and energy
storage, can be switched to the inertia emulation mode when the detected
frequency deviation exceeds a pre-designed threshold, i.e. dead band, to
support the frequency response of a power grid. This letter proposes an
approach to derive the emulat... | 1611.02698v1 |
2016-12-09 | Ornstein-Uhlenbeck Process with Fluctuating Damping | This paper studies Langevin equation with random damping due to
multiplicative noise and its solution. Two types of multiplicative noise,
namely the dichotomous noise and fractional Gaussian noise are considered.
Their solutions are obtained explicitly, with the expressions of the mean and
covariance determined explici... | 1612.03013v3 |
2016-12-20 | Symmetry group classification and optimal reduction of a class of damped Timoshenko beam system with a nonlinear rotational moment | We consider a nonlinear Timoshenko system of partial differential equations
(PDEs) with a frictional damping term in rotation angle. The nonlinearity is
due to the arbitrary dependence on the rotation moment. A Lie symmetry group
classification of the arbitrary function of rotation moment is presented. An
optimal syste... | 1612.06775v1 |
2017-03-14 | Landau damping in the multiscale Vlasov theory | Vlasov kinetic theory is extended by adopting an extra one particle
distribution function as an additional state variable characterizing the
micro-turbulence internal structure. The extended Vlasov equation keeps the
reversibility, the Hamiltonian structure, and the entropy conservation of the
original Vlasov equation.... | 1703.04577v2 |
2017-03-15 | Energy decay and diffusion phenomenon for the asymptotically periodic damped wave equation | We prove local and global energy decay for the asymptotically periodic damped
wave equation on the Euclidean space. Since the behavior of high frequencies is
already mostly understood, this paper is mainly about the contribution of low
frequencies. We show in particular that the damped wave behaves like a solution
of a... | 1703.05112v1 |
2017-04-03 | Linear inviscid damping and vorticity depletion for shear flows | In this paper, we prove the linear damping for the 2-D Euler equations around
a class of shear flows under the assumption that the linearized operator has no
embedding eigenvalues. For the symmetric flows, we obtain the explicit decay
estimates of the velocity, which is the same as one for monotone shear flows.
We conf... | 1704.00428v1 |
2017-04-25 | Diffusion phenomena for the wave equation with space-dependent damping term growing at infinity | In this paper, we study the asymptotic behavior of solutions to the wave
equation with damping depending on the space variable and growing at the
spatial infinity. We prove that the solution is approximated by that of the
corresponding heat equation as time tends to infinity. The proof is based on
semigroup estimates f... | 1704.07650v1 |
2017-06-05 | Mixed finite elements for global tide models with nonlinear damping | We study mixed finite element methods for the rotating shallow water
equations with linearized momentum terms but nonlinear drag. By means of an
equivalent second-order formulation, we prove long-time stability of the system
without energy accumulation. We also give rates of damping in unforced systems
and various cont... | 1706.01352v1 |
2017-06-13 | Uniform energy decay for wave equations with unbounded damping coefficients | We consider the Cauchy problem for wave equations with unbounded damping
coefficients in the whole space. For a general class of unbounded damping
coefficients, we derive uniform total energy decay estimates together with a
unique existence result of a weak solution. In this case we never impose strong
assumptions such... | 1706.03942v1 |
2017-06-15 | Fractional Driven Damped Oscillator | The resonances associated with a fractional damped oscillator which is driven
by an oscillatory external force are studied. It is shown that such resonances
can be manipulated by tuning up either the coefficient of the fractional
damping or the order of the corresponding fractional derivatives. | 1706.08596v1 |
2017-07-11 | Stability of partially locked states in the Kuramoto model through Landau damping with Sobolev regularity | The Kuramoto model is a mean-field model for the synchronisation behaviour of
oscillators, which exhibits Landau damping. In a recent work, the nonlinear
stability of a class of spatially inhomogeneous stationary states was shown
under the assumption of analytic regularity. This paper proves the nonlinear
Landau dampin... | 1707.03475v2 |
2017-08-27 | Global well-posedness for the semilinear wave equation with time dependent damping in the overdamping case | We study global existence of solutions to the Cauchy problem for the wave
equation with time-dependent damping and a power nonlinearity in the
overdamping case. We prove the global well-posedness for small data in the
energy space for the whole energy-subcritical case. This result implies that
small data blow-up does n... | 1708.08044v2 |
2017-09-04 | A note on the blowup of scale invariant damping wave equation with sub-Strauss exponent | We concern the blow up problem to the scale invariant damping wave equations
with sub-Strauss exponent. This problem has been studied by Lai, Takamura and
Wakasa (\cite{Lai17}) and Ikeda and Sobajima \cite{Ikedapre} recently. In
present paper, we extend the blowup exponent from $p_F(n)\leq p<p_S(n+2\mu)$ to
$1<p<p_S(n+... | 1709.00866v2 |
2017-09-13 | Life-span of blowup solutions to semilinear wave equation with space-dependent critical damping | This paper is concerned with the blowup phenomena for initial value problem
of semilinear wave equation with critical space-dependent damping term
(DW:$V$). The main result of the present paper is to give a solution of the
problem and to provide a sharp estimate for lifespan for such a solution when
$\frac{N}{N-1}<p\le... | 1709.04401v1 |
2017-11-01 | Life-Span of Semilinear Wave Equations with Scale-invariant Damping: Critical Strauss Exponent Case | The blow up problem of the semilinear scale-invariant damping wave equation
with critical Strauss type exponent is investigated. The life span is shown to
be: $T(\varepsilon)\leq C\exp(\varepsilon^{-2p(p-1)})$ when $p=p_S(n+\mu)$ for
$0<\mu<\frac{n^2+n+2}{n+2}$. This result completes our previous study
\cite{Tu-Lin} on... | 1711.00223v1 |
2017-11-14 | Spin-Noise and Damping in Individual Metallic Ferromagnetic Nanoparticles | We introduce a highly sensitive and relatively simple technique to observe
magnetization motion in single Ni nanoparticles, based on charge sensing by
electron tunneling at millikelvin temperature. Sequential electron tunneling
via the nanoparticle drives nonequilibrium magnetization dynamics, which
induces an effectiv... | 1711.05142v1 |
2017-12-04 | Graviton-mediated dark matter model explanation the DAMPE electron excess and search at $e^+e^-$ colliders | The very recent result of the DAMPE cosmic ray spectrum of electrons shows a
narrow bump above the background at around 1.4 TeV. We attempt to explain the
DAMPE electron excess in a simplified Kaluza-Klein graviton-mediated dark
matter model, in which the graviton only interacts with leptons and dark
matter. The relate... | 1712.01143v1 |
2017-12-13 | On nonlinear damped wave equations for positive operators. I. Discrete spectrum | In this paper we study a Cauchy problem for the nonlinear damped wave
equations for a general positive operator with discrete spectrum. We derive the
exponential in time decay of solutions to the linear problem with decay rate
depending on the interplay between the bottom of the operator's spectrum and
the mass term. C... | 1712.05009v1 |
2018-03-14 | Damped Newton's Method on Riemannian Manifolds | A damped Newton's method to find a singularity of a vector field in
Riemannian setting is presented with global convergence study. It is ensured
that the sequence generated by the proposed method reduces to a sequence
generated by the Riemannian version of the classical Newton's method after a
finite number of iteratio... | 1803.05126v2 |
2018-04-19 | Damping of magnetization dynamics by phonon pumping | We theoretically investigate pumping of phonons by the dynamics of a magnetic
film into a non-magnetic contact. The enhanced damping due to the loss of
energy and angular momentum shows interference patterns as a function of
resonance frequency and magnetic film thickness that cannot be described by
viscous ("Gilbert")... | 1804.07080v2 |
2018-05-29 | Asymptotic profile of solutions for strongly damped Klein-Gordon equations | We consider the Cauchy problem in the whole space for strongly damped
Klein-Gordon equations. We derive asymptotic profles of solutions with weighted
initial data by a simple method introduced by R. Ikehata. The obtained results
show that the wave effect will be weak because of the mass term, especially in
the low dime... | 1805.11975v1 |
2018-06-18 | Damped second order flow applied to image denoising | In this paper, we introduce a new image denoising model: the damped flow
(DF), which is a second order nonlinear evolution equation associated with a
class of energy functionals of image. The existence, uniqueness and
regularization property of DF are proven. For the numerical implementation,
based on the St\"{o}rmer-V... | 1806.06732v2 |
2018-07-10 | Cyclotron Damping along an Uniform Magnetic Field | We prove cyclotron damping for the collisionless Vlasov-Maxwell equations on
$\mathbb{T}_{x}^{3}\times\mathbb{R}_{v}^{3}$ under the assumptions that the
electric induction is zero and $(\mathcal{\mathbf{PSC}})$ holds. It is a
crucial step to solve the stability problem of the Vlasov-Maxwell equations.
Our proof is base... | 1807.05254v3 |
2018-07-17 | On the blow-up for critical semilinear wave equations with damping in the scattering case | We consider the Cauchy problem for semilinear wave equations with variable
coefficients and time-dependent scattering damping in $\mathbf{R}^n$, where
$n\geq 2$. It is expected that the critical exponent will be Strauss' number
$p_0(n)$, which is also the one for semilinear wave equations without damping
terms. Lai and... | 1807.06164v1 |
2018-08-22 | Radiation Damping of a Yang-Mills Particle Revisited | The problem of a color-charged point particle interacting with a four
dimensional Yang-Mills gauge theory is revisited. The radiation damping is
obtained inspired in the Dirac's computation. The difficulties in the
non-abelian case were solved by using an ansatz for the Li\'enard-Wiechert
potentials, already used in th... | 1808.07533v2 |
2018-08-28 | Enhancement of zonal flow damping due to resonant magnetic perturbations in the background of an equilibrium $E \times B$ sheared flow | Using a parametric interaction formalism, we show that the equilibrium
sheared rotation can enhance the zonal flow damping effect found in Ref. [M.
Leconte and P.H. Diamond, \emph{Phys. Plasmas} 19, 055903 (2012)]. This
additional damping contribution is proportional to $(L_s/L_V)^2 \times \delta
B_r^2 / B^2$, where $L... | 1808.09110v1 |
2018-08-30 | Optimal indirect stability of a weakly damped elastic abstract system of second order equations coupled by velocities | In this paper, by means of the Riesz basis approach, we study the stability
of a weakly damped system of two second order evolution equations coupled
through the velocities. If the fractional order damping becomes viscous and the
waves propagate with equal speeds, we prove exponential stability of the system
and, other... | 1808.10256v1 |
2018-09-10 | Linear inviscid damping for the $β$-plane equation | In this paper, we study the linear inviscid damping for the linearized
$\beta$-plane equation around shear flows. We develop a new method to give the
explicit decay rate of the velocity for a class of monotone shear flows. This
method is based on the space-time estimate and the vector field method in sprit
of the wave ... | 1809.03065v1 |
2018-10-14 | Critical exponent for nonlinear damped wave equations with non-negative potential in 3D | We are studying possible interaction of damping coefficients in the
subprincipal part of the linear 3D wave equation and their impact on the
critical exponent of the corresponding nonlinear Cauchy problem with small
initial data. The main new phenomena is that certain relation between these
coefficients may cause very ... | 1810.05956v1 |
2018-10-23 | Perfect absorption of water waves by linear or nonlinear critical coupling | We report on experiments of perfect absorption for surface gravity waves
impinging a wall structured by a subwavelength resonator. By tuning the
geometry of the resonator, a balance is achieved between the radiation damping
and the intrinsic viscous damping, resulting in perfect absorption by critical
coupling. Besides... | 1810.09884v1 |
2018-12-16 | Damping of sound waves by bulk viscosity in reacting gases | The very long standing problem of sound waves propagation in fluids is
reexamined. In particular, from the analysis of the wave damping in reacting
gases following the work of Einsten \citep{Ein}, it is found that the damping
due to the chemical reactions occurs nonetheless the second (bulk) viscosity
introduced by Lan... | 1812.06478v1 |
2019-02-27 | Forward Discretely Self-Similar Solutions of the MHD Equations and the Viscoelastic Navier-Stokes Equations with Damping | In this paper, we prove the existence of forward discretely self-similar
solutions to the MHD equations and the viscoelastic Navier-Stokes equations
with damping with large weak $L^3$ initial data. The same proving techniques
are also applied to construct self-similar solutions to the MHD equations and
the viscoelastic... | 1902.10771v3 |
2019-03-11 | The effect of magnetic twist on resonant absorption of slow sausage waves in magnetic flux tubes | Observations show that twisted magnetic flux tubes are present throughout the
sun's atmosphere. The main aim of this work is to obtain the damping rate of
sausage modes in the presence of magnetic twist. Using the connection formulae
obtained by Sakurai et al. (1991), we investigate resonant absorption of the
sausage m... | 1903.04171v1 |
2019-03-14 | Endpoint Strichartz estimate for the damped wave equation and its application | Recently, the Strichartz estimates for the damped wave equation was obtained
by the first author except for the wave endpoint case. In the present paper, we
give the Strichartz estimate in the wave endpoint case. We slightly modify the
argument of Keel--Tao. Moreover, we apply the endpoint Strichartz estimate to
the un... | 1903.05891v2 |
2019-04-02 | Linear inviscid damping in Gevrey spaces | We prove linear inviscid damping near a general class of monotone shear flows
in a finite channel, in Gevrey spaces. It is an essential step towards proving
nonlinear inviscid damping for general shear flows that are not close to the
Couette flow, which is a major open problem in 2d Euler equations. | 1904.01188v2 |
2019-04-16 | Damping modes of harmonic oscillator in open quantum systems | Through a set of generators that preserves the hermiticity and trace of
density matrices, we analyze the damping of harmonic oscillator in open quantum
systems into four modes, distinguished by their specific effects on the
covariance matrix of position and momentum of the oscillator. The damping modes
could either cau... | 1904.07452v2 |
2019-05-20 | Stabilization of two strongly coupled hyperbolic equations in exterior domains | In this paper we study the behavior of the total energy and the $L^2$-norm of
solutions of two coupled hyperbolic equations by velocities in exterior
domains. Only one of the two equations is directly damped by a localized
damping term. We show that, when the damping set contains the coupling one and
the coupling term ... | 1905.08370v1 |
2019-06-02 | Mixed control of vibrational systems | We consider new performance measures for vibrational systems based on the
$H_2$ norm of linear time invariant systems. New measures will be used as an
optimization criterion for the optimal damping of vibrational systems. We
consider both theoretical and concrete cases in order to show how new measures
stack up against... | 1906.00503v1 |
2019-06-27 | Comments on the linear modified Poisson-Boltzmann equation in electrolyte solution theory | Three analytic results are proposed for a linear form of the modified
Poisson-Boltzmann equation in the theory of bulk electrolytes. Comparison is
also made with the mean spherical approximation results. The linear theories
predict a transition of the mean electrostatic potential from a
Debye-H\"{u}ckel type damped exp... | 1906.11584v1 |
2019-09-19 | Growth rate and gain of stimulated Brillouin scattering considering nonlinear Landau damping due to particle trapping | Growth rate and gain of SBS considering the reduced Landau damping due to
particle trapping has been proposed to predict the growth and average level of
SBS reflectivity. Due to particle trapping, the reduced Landau damping has been
taken used of to calculate the gain of SBS, which will make the simulation data
of SBS ... | 1909.11606v1 |
2019-11-26 | Pullback Attractors for a Critical Degenerate Wave Equation with Time-dependent Damping | The aim of this paper is to analyze the long-time dynamical behavior of the
solution for a degenerate wave equation with time-dependent damping term
$\partial_{tt}u + \beta(t)\partial_tu = \mathcal{L}u(x,t) + f(u)$ on a bounded
domain $\Omega\subset\mathbb{R}^N$ with Dirichlet boundary conditions. Under
some restrictio... | 1911.11432v1 |
2019-12-18 | Blow-up criteria for linearly damped nonlinear Schrödinger equations | We consider the Cauchy problem for linearly damped nonlinear Schr\"odinger
equations
\[ i\partial_t u + \Delta u + i a u= \pm |u|^\alpha u, \quad (t,x) \in
[0,\infty) \times \mathbb{R}^N, \] where $a>0$ and $\alpha>0$. We prove the
global existence and scattering for a sufficiently large damping parameter in
the ener... | 1912.08752v2 |
2020-01-17 | Bounding the Classical Capacity of Multilevel Damping Quantum Channels | A recent method to certify the classical capacity of quantum communication
channels is applied for general damping channels in finite dimension. The
method compares the mutual information obtained by coding on the computational
and a Fourier basis, which can be obtained by just two local measurement
settings and classi... | 2001.06486v2 |
2020-01-27 | Robustness of polynomial stability of damped wave equations | In this paper we present new results on the preservation of polynomial
stability of damped wave equations under addition of perturbing terms. We in
particular introduce sufficient conditions for the stability of perturbed
two-dimensional wave equations on rectangular domains, a one-dimensional weakly
damped Webster's e... | 2001.10033v3 |
2020-02-09 | Fujita modified exponent for scale invariant damped semilinear wave equations | The aim of this paper is to prove a blow up result of the solution for a
semilinear scale invariant damped wave equation under a suitable decay
condition on radial initial data. The admissible range for the power of the
nonlinear term depends both on the damping coefficient and on the pointwise
decay order of the initi... | 2002.03418v2 |
2020-02-16 | Blow up results for semi-linear structural damped wave model with nonlinear memory | This article is to study the nonexistence of global solutions to semi-linear
structurally damped wave equation with nonlinear memory in $\R^n$ for any space
dimensions $n\ge 1$ and for the initial arbitrarily small data being subject to
the positivity assumption. We intend to apply the method of a modified test
functio... | 2002.06582v1 |
2020-03-04 | Existence and uniqueness of solutions to the damped Navier-Stokes equations with Navier boundary conditions for three dimensional incompressible fluid | In this article, we study the solutions of the damped Navier--Stokes equation
with Navier boundary condition in a bounded domain $\Omega$ in $\mathbb{R}^3$
with smooth boundary. The existence of the solutions is global with the damped
term $\vartheta |u|^{\beta-1}u, \vartheta >0.$ The regularity and uniqueness of
solut... | 2003.01903v1 |
2020-04-22 | Logarithmic stabilization of an acoustic system with a damping term of Brinkman type | We study the problem of stabilization for the acoustic system with a
spatially distributed damping. Without imposing any hypotheses on the
structural properties of the damping term, we identify logarithmic decay of
solutions with growing time. Logarithmic decay rate is shown by using a
frequency domain method and combi... | 2004.10669v1 |
2020-05-24 | A transmission problem for the Timoshenko system with one local Kelvin-Voigt damping and non-smooth coefficient at the interface | In this paper, we study the indirect stability of Timoshenko system with
local or global Kelvin-Voigt damping, under fully Dirichlet or mixed boundary
conditions. Unlike the results of H. L. Zhao, K. S. Liu, and C. G. Zhang and of
X. Tian and Q. Zhang, in this paper, we consider the Timoshenko system with
only one loca... | 2005.12756v1 |
2020-06-09 | Lifespan of solutions to a damped fourth-order wave equation with logarithmic nonlinearity | This paper is devoted to the lifespan of solutions to a damped fourth-order
wave equation with logarithmic nonlinearity $$u_{tt}+\Delta^2u-\Delta
u-\omega\Delta u_t+\alpha(t)u_t=|u|^{p-2}u\ln|u|.$$ Finite time blow-up
criteria for solutions at both lower and high initial energy levels are
established, and an upper boun... | 2006.05006v1 |
2020-07-05 | Oscillation of damped second order quasilinear wave equations with mixed arguments | Following the previous work [1], we investigate the impact of damping on the
oscillation of smooth solutions to some kind of quasilinear wave equations with
Robin and Dirichlet boundary condition. By using generalized Riccati
transformation and technical inequality method, we give some sufficient
conditions to guarante... | 2007.02284v1 |
2020-07-08 | A competition on blow-up for semilinear wave equations with scale-invariant damping and nonlinear memory term | In this paper, we investigate blow-up of solutions to semilinear wave
equations with scale-invariant damping and nonlinear memory term in
$\mathbb{R}^n$, which can be represented by the Riemann-Liouville fractional
integral of order $1-\gamma$ with $\gamma\in(0,1)$. Our main interest is to
study mixed influence from da... | 2007.03954v2 |
2020-08-02 | Quantum capacity analysis of multi-level amplitude damping channels | The set of Multi-level Amplitude Damping (MAD) quantum channels is introduced
as a generalization of the standard qubit Amplitude Damping Channel to quantum
systems of finite dimension $d$. In the special case of $d=3$, by exploiting
degradability, data-processing inequalities, and channel isomorphism, we
compute the a... | 2008.00477v3 |
2020-08-11 | An inverse spectral problem for a damped wave operator | This paper proposes a new and efficient numerical algorithm for recovering
the damping coefficient from the spectrum of a damped wave operator, which is a
classical Borg-Levinson inverse spectral problem. The algorithm is based on
inverting a sequence of trace formulas, which are deduced by a recursive
formula, bridgin... | 2008.04523v1 |
2020-08-17 | Asymptotic profiles and singular limits for the viscoelastic damped wave equation with memory of type I | In this paper, we are interested in the Cauchy problem for the viscoelastic
damped wave equation with memory of type I. By applying WKB analysis and
Fourier analysis, we explain the memory's influence on dissipative structures
and asymptotic profiles of solutions to the model with weighted $L^1$ initial
data. Furthermo... | 2008.07151v1 |
2020-08-18 | A class of Finite difference Methods for solving inhomogeneous damped wave equations | In this paper, a class of finite difference numerical techniques is presented
to solve the second-order linear inhomogeneous damped wave equation. The
consistency, stability, and convergences of these numerical schemes are
discussed. The results obtained are compared to the exact solution, ordinary
explicit, implicit f... | 2008.08043v2 |
2020-09-10 | Blow-up results for semilinear damped wave equations in Einstein-de Sitter spacetime | We prove by using an iteration argument some blow-up results for a semilinear
damped wave equation in generalized Einstein-de Sitter spacetime with a
time-dependent coefficient for the damping term and power nonlinearity. Then,
we conjecture an expression for the critical exponent due to the main blow-up
results, which... | 2009.05372v1 |
2020-09-11 | Asymptotic profiles for a wave equation with parameter dependent logarithmic damping | We study a nonlocal wave equation with logarithmic damping which is rather
weak in the low frequency zone as compared with frequently studied strong
damping case. We consider the Cauchy problem for this model in the whole space
and we study the asymptotic profile and optimal estimates of the solutions and
the total ene... | 2009.06395v1 |
2020-09-17 | Sensitivity of steady states in a degenerately-damped stochastic Lorenz system | We study stability of solutions for a randomly driven and degenerately damped
version of the Lorenz '63 model. Specifically, we prove that when damping is
absent in one of the temperature components, the system possesses a unique
invariant probability measure if and only if noise acts on the convection
variable. On the... | 2009.08429v1 |
2021-01-23 | Oscillation time and damping coefficients in a nonlinear pendulum | We establish a relationship between the normalized damping coefficients and
the time that takes a nonlinear pendulum to complete one oscillation starting
from an initial position with vanishing velocity. We establish some conditions
on the nonlinear restitution force so that this oscillation time does not
depend monoto... | 2101.09400v2 |
2021-02-20 | Lifespan estimates for semilinear wave equations with space dependent damping and potential | In this work, we investigate the influence of general damping and potential
terms on the blow-up and lifespan estimates for energy solutions to power-type
semilinear wave equations. The space-dependent damping and potential functions
are assumed to be critical or short range, spherically symmetric perturbation.
The blo... | 2102.10257v1 |
2021-02-24 | Attractors for locally damped Bresse systems and a unique continuation property | This paper is devoted to Bresse systems, a robust model for circular beams,
given by a set of three coupled wave equations. The main objective is to
establish the existence of global attractors for dynamics of semilinear
problems with localized damping. In order to deal with localized damping a
unique continuation prop... | 2102.12025v1 |
2021-03-09 | Global weak solution of 3D-NSE with exponential damping | In this paper we prove the global existence of incompressible Navier-Stokes
equations with damping $\alpha (e^{\beta |u|^2}-1)u$, where we use Friedrich
method and some new tools. The delicate problem in the construction of a global
solution, is the passage to the limit in exponential nonlinear term. To solve
this prob... | 2103.05388v1 |
2021-05-03 | Enhanced and unenhanced dampings of the Kolmogorov flow | In the present study, Kolmogorov flow represents the stationary sinusoidal
solution $(\sin y,0)$ to a two-dimensional spatially periodic Navier-Stokes
system, driven by an external force. This system admits the additional
non-stationary solution $(\sin y,0)+e^{-\nu t} (\sin y,0)$, which tends
exponentially to the Kolmo... | 2105.00730v3 |
2021-05-06 | On Linear Damping Around Inhomogeneous Stationary States of the Vlasov-HMF Model | We study the dynamics of perturbations around an inhomogeneous stationary
state of the Vlasov-HMF (Hamiltonian Mean-Field) model, satisfying a linearized
stability criterion (Penrose criterion). We consider solutions of the
linearized equation around the steady state, and prove the algebraic decay in
time of the Fourie... | 2105.02484v1 |
2021-05-31 | Blowup of Solutions to a Damped Euler Equation with Homogeneous Three-Point Boundary Condition | It has been established that solutions to the inviscid Proudman-Johnson
equation subject to a homogeneous three-point boundary condition can develop
singularities in finite time. In this paper, we consider the possibility of
singularity formation in solutions of the generalized, inviscid
Proudman-Johnson equation with ... | 2106.00068v1 |
2021-06-16 | Sharp upper and lower bounds of the attractor dimension for 3D damped Euler-Bardina equations | The dependence of the fractal dimension of global attractors for the damped
3D Euler--Bardina equations on the regularization parameter $\alpha>0$ and
Ekman damping coefficient $\gamma>0$ is studied. We present explicit upper
bounds for this dimension for the case of the whole space, periodic boundary
conditions, and t... | 2106.09077v1 |
2021-06-23 | Damping of the Franz-Keldysh oscillations in the presence of disorder | Franz-Keldysh oscillations of the optical absorption in the presence of
short-range disorder are studied theoretically. The magnitude of the effect
depends on the relation between the mean-free path in a zero field and the
distance between the turning points in electric field. Damping of the
Franz-Keldysh oscillations ... | 2106.12691v1 |
2021-06-25 | Perturbed primal-dual dynamics with damping and time scaling coefficients for affine constrained convex optimization problems | In Hilbert space, we propose a family of primal-dual dynamical system for
affine constrained convex optimization problem. Several damping coefficients,
time scaling coefficients, and perturbation terms are thus considered. By
constructing the energy functions, we investigate the convergence rates with
different choices... | 2106.13702v1 |
2021-07-01 | Event-triggering mechanism to damp the linear wave equation | This paper aims at proposing a sufficient matrix inequality condition to
carry out the global exponential stability of the wave equation under an
event-triggering mechanism that updates a damping source term. The damping is
distributed in the whole space but sampled in time. The wellposedness of the
closed-loop event-t... | 2107.00292v1 |
2022-01-28 | Quantum metrology with a non-linear kicked Mach-Zehnder interferometer | We study the sensitivity of a Mach-Zehnder interferometer that contains in
addition to the phase shifter a non-linear element. By including both elements
in a cavity or a loop that the light transverses many times, a non-linear
kicked version of the interferometer arises. We study its sensitivity as
function of the pha... | 2201.12255v1 |
2022-02-27 | The time asymptotic expansion for the compressible Euler equations with time-dependent damping | In this paper, we study the compressible Euler equations with time-dependent
damping $-\frac{1}{(1+t)^{\lambda}}\rho u$. We propose a time asymptotic
expansion around the self-similar solution of the generalized porous media
equation (GPME) and rigorously justify this expansion as $\lambda \in
(\frac17,1)$. In other wo... | 2202.13385v1 |
2022-03-12 | Stability for nonlinear wave motions damped by time-dependent frictions | We are concerned with the dynamical behavior of solutions to semilinear wave
systems with time-varying damping and nonconvex force potential. Our result
shows that the dynamical behavior of solution is asymptotically stable without
any bifurcation and chaos. And it is a sharp condition on the damping
coefficient for th... | 2203.06312v1 |
2022-03-30 | A Toy Model for Damped Water Waves | We consider a toy model for a damped water waves system in a domain $\Omega_t
\subset \mathbb{T} \times \mathbb{R}$. The toy model is based on the
paradifferential water waves equation derived in the work of
Alazard-Burq-Zuily. The form of damping we utilize we utilize is a modified
sponge layer proposed for the three-... | 2203.16645v1 |
2022-05-10 | Global attractor for the weakly damped forced Kawahara equation on the torus | We study the long time behaviour of solutions for the weakly damped forced
Kawahara equation on the torus. More precisely, we prove the existence of a
global attractor in $L^2$, to which as time passes all solutions draw closer.
In fact, we show that the global attractor turns out to lie in a smoother space
$H^2$ and b... | 2205.04642v1 |
2022-06-07 | Decay property of solutions to the wave equation with space-dependent damping, absorbing nonlinearity, and polynomially decaying data | We study the large time behavior of solutions to the semilinear wave equation
with space-dependent damping and absorbing nonlinearity in the whole space or
exterior domains. Our result shows how the amplitude of the damping
coefficient, the power of the nonlinearity, and the decay rate of the initial
data at the spatia... | 2206.03218v2 |
2022-10-24 | The time asymptotic expansion for the compressible Euler equations with damping | In 1992, Hsiao and Liu \cite{Hsiao-Liu-1} firstly showed that the solution to
the compressible Euler equations with damping time-asymptotically converges to
the diffusion wave $(\bar v, \bar u)$ of the porous media equation. In
\cite{Geng-Huang-Jin-Wu}, we proposed a time-asymptotic expansion around the
diffusion wave ... | 2210.13157v1 |
2022-12-18 | Exponential decay of solutions of damped wave equations in one dimensional space in the $L^p$ framework for various boundary conditions | We establish the decay of the solutions of the damped wave equations in one
dimensional space for the Dirichlet, Neumann, and dynamic boundary conditions
where the damping coefficient is a function of space and time. The analysis is
based on the study of the corresponding hyperbolic systems associated with the
Riemann ... | 2212.09164v1 |
2023-02-09 | A remark on the logarithmic decay of the damped wave and Schrödinger equations on a compact Riemannian manifold | In this paper we consider a compact Riemannian manifold (M, g) of class C 1
$\cap$ W 2,$\infty$ and the damped wave or Schr\"odinger equations on M , under
the action of a damping function a = a(x). We establish the following fact: if
the measure of the set {x $\in$ M ; a(x) = 0} is strictly positive, then the
decay in... | 2302.04498v1 |
2023-03-02 | Using vibrating wire in non-linear regime as a thermometer in superfluid $^3$He-B | Vibrating wires are common temperature probes in $^3$He experiments. By
measuring mechanical resonance of a wire driven by AC current in magnetic field
one can directly obtain temperature-dependent viscous damping. This is easy to
do in a linear regime where wire velocity is small enough and damping force is
proportion... | 2303.01189v1 |
2023-04-06 | A turbulent study for a damped Navier-Stokes equation: turbulence and problems | In this article we consider a damped version of the incompressible
Navier-Stokes equations in the whole three-dimensional space with a
divergence-free and time-independent external force. Within the framework of a
well-prepared force and with a particular choice of the damping parameter, when
the Grashof numbers are la... | 2304.03134v1 |
2023-05-03 | Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions | We establish the exponential decay of the solutions of the damped wave
equations in one-dimensional space where the damping coefficient is a
nowhere-vanishing function of space. The considered PDE is associated with
several dynamic boundary conditions, also referred to as Wentzell/Ventzel
boundary conditions in the lit... | 2305.01969v2 |
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