相关论文: A note on local energy decay results for wave equa…

In this paper we study spectral properties associated to Schrodinger operator with potential that is an exponential decaying function. As applications we prove local energy decay for solutions to the perturbed wave equation and lack of…

We consider Morawetz estimates for weighted energy decay of solutions to the wave equation on scattering manifolds (i.e., those with large conic ends). We show that a Morawetz estimate persists for solutions that are localized at low…

We consider the wave equation with a damping term on a partially rectangular planar domain, assuming that the damping is concentrated close to the non-rectangular part of the domain. Polynomial decay estimates for the energy of the solution…

In this paper we analyze the long time behavior of a wave equation with local Kelvin-Voigt Damping. Through introducing proper class symbol and pseudo-differential calculus, we obtain a Carleman estimate, and then establish an estimate on…

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…

We consider the initial-value problem for a one-dimensional wave equation with coefficients that are positive, constant outside of an interval, and have bounded variation (BV). Under the assumption of compact support of the initial data, we…

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…

We study the rate of decay of the energy functional of solutions of the wave equation with localized damping and a external force. We prove that the decay rates of the energy functional is determined from a forced differential equation.

We consider solutions to the initial value problem associated to the intermediate long wave (ILW) equation. We establish persistence properties of the solution flow in weighted Sobolev spaces, and show that they are sharp. We also deal with…

This paper is concerned with the energy decay and the finite time blow-up of the solution to a viscoelastic wave equation with polynomial nonlinearity and weak damping. We establish explicit and general decay results for the solutions by…

Energy decay is established for the damped wave equation on compact Riemannian manifolds where the damping coefficient is allowed to depend on time. Using a time dependent observability inequality, it is shown that the energy of solutions…

We study the linear wave equation on a class of spatially homogeneous and isotropic Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetimes in the decelerated regime with spatial topology $\mathbb{R}^3$. Employing twisted $t$-weighted…

In earlier works, we have shown the uniform decay of the local energy of the damped wave equation in exterior domain when the damper is spatially localized near captive rays. In order to have uniform decay of the total energy, the damper…

This paper is devoted to study a nonlinear wave equation with boundary conditions of two-point type. First, we state two local existence theorems and under suitable conditions, we prove that any weak solutions with negative initial energy…

In this paper, we investigate the stabilization of a locally coupled wave equations with local viscoelastic damping of past history type acting only in one equation via non smooth coefficients. First, using a general criteria of…

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…

We prove a weighted a priori energy estimate for the two dimensional water-waves problem with contact points in the absence of gravity and surface tension. When the surface graph function and its time derivative have some decay near the…

The goal of this paper is to study a nonlinear viscoelastic wave equation with strong damping, time-varying delay and dynamical boundary condition. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we then…

Consider the mixed problem with Dirichelet condition associated to the wave equation $\partial_t^2u-\Div_{x}(a(t,x)\nabla_{x}u)=0$, where the scalar metric $a(t,x)$ is $T$-periodic in $t$ and uniformly equal to 1 outside a compact set in…

We consider finite-energy solutions to the defocusing nonlinear wave equation in two dimensional space. We prove that almost all energy moves to the infinity at almost the light speed as time tends to infinity. In addition, the…