Related papers: Semigroup decay for the wave equation with unbound…
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are…
We consider the strongly damped Klein Gordon equation for defocusing nonlinearity and we study the asymptotic behaviour of the energy for periodic solutions. We prove first the exponential decay to zero for zero mean solutions. Then, we…
We present a new and simple bound for the exponential decay of second order systems using the spectral shift. This result is applied to finite matrices as well as to partial differential equations of Mathematical Physics. The type of the…
We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their well-posedness and describe some…
We study the Cauchy problem for the nonlinear damped wave equation and establish the large data local well-posedness and small data global well-posedness with slowly decaying initial data. We also prove that the asymptotic profile of the…
We prove local decay estimates for the wave equation in the asymptotically Euclidean setting. In even dimensions we go beyond the optimal decay by providing the large time asymptotic profile, given by a solution of the free wave equation.…
In this paper we study the behavior of the energy of solutions of the wave equation with localized damping in exterior domain. We assume that the damper is positive at infinity. Under the Geometric Control Condition of Bardos et al (1992),…
We study the decay of global energy for the wave equation with H\"older continuous damping placed on the $C^{1,1}$-boundary of compact and non-compact waveguides with star-shaped cross-sections. We show there is sharp $t^{-1/2}$-decay when…
In this paper we study a semilinear wave equation with nonlinear, time-dependent damping in one space dimension. For this problem, we prove a well-posedness result in $W^{1,\infty}$ in the space-time domain $(0,1)\times [0,+\infty)$. Then…
In this paper, we investigate the direct and indirect stability of locally coupled wave equations with local viscous damping on cylindrical and non-regular domains without any geometric control condition. If only one equation is damped, we…
We consider a coupled wave system with partial Kelvin-Voigt damping in the interval (-1,1), where one wave is dissipative and the other does not. When the damping is effective in the whole domain (-1,1) it was proven in H.Portillo Oquendo…
We prove integrated local energy decay for solutions of the damped wave equation with time-dependent damping satisfying an appropriate generalization of the geometric control condition on asymptotically flat, stationary space-times. We…
In this paper, we consider the well-posedness and stability of a one-dimensional system of degenerate wave equations coupled via zero order terms with one boundary fractional damping acting on one end only. We prove optimal polynomial…
This paper is concerned with the analysis of a one dimensional wave equation $z_{tt}-z_{xx}=0$ on $[0,1]$ with a Dirichlet condition at $x=0$ and a damping acting at $x=1$ which takes the form $(z_t(t,1),-z_x(t,1))\in\Sigma$ for every…
We study the Cauchy problem for the semi-linear damped wave equation in any space dimension. We assume that the time-dependent damping term is effective. We prove the global existence of small energy data solutions in the supercritical…
We consider the global Cauchy problem for a two-component system of cubic semilinear wave equations in two space dimensions. We give a criterion for large time non-decay of the energy for small amplitude solutions in terms of the radiation…
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…
For fractional wave equations with low H\"older regularity damping, we establish quantitative energy decay rates for their solutions when the geometric control condition holds. The energy decay rates depend explicitly on the H\"older…
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…
A strongly damped wave equation including the displacement depending nonlinear damping term and nonlinear interaction function is considered. The main aim of the note is to show that under the standard dissipativity restrictions on the…