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We consider the transmission problem for a coupled system of undamped and structurally damped plate equations in two sufficiently smooth and bounded subdomains. It is shown that, independently of the size of the damped part, the damping is…
We develop an eigenvalue-based approach for the stability assessment and stabilization of linear systems with multiple delays and periodic coefficient matrices. Delays and period are assumed commensurate numbers, such that the Floquet…
The focal point of this paper is to theoretically investigate and numerically validate the effect of time delay on the exponential stabilization of a class of coupled hyperbolic systems with delayed and non-delayed dampings. The class in…
We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…
We investigate stability properties of indirectly damped systems of evolution equations in Hilbert spaces, under new compatibility assumptions. We prove polynomial decay for the energy of solutions and optimize our results by interpolation…
This paper is devoted to the exponential stability for one-dimensional linear wave equations with in-domain localized damping and several types of Wentzell (or dynamic) boundary conditions. In a quite general boundary setting, we establish…
We consider a pointwise stabilization problem for a coupled wave and plate equations. We prove under rather general assumptions, that such systems can stabilized so as to have arbitrarily high decay rates and are exactly controllable. We…
In this paper, we investigate a system composed of two degenerate wave equations which are connected at one point. By introducing some inequalities on the weighted spaces and employing the frequency domain method, we prove that the system…
In this paper, we study the defocusing nonlinear Schr\"{o}dinger equation with a locally distributed damping on a smooth bounded domain as well as on the whole space and on an exterior domain. We first construct approximate solutions using…
This paper is devoted to the study of the stability and stabilizability of heat equation in non-cylindrical domain. The interesting thing is that there is a class of initial values such that the system is no longer exponentially stable. The…
We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…
The purpose of this work is to investigate the exponential stability of a second order coupled wave equations by laplacian with one locally internal viscous damping. Firstly, using a unique continuation theorem combined with a Carleman…
We study the time-asymptotic behavior of linear hyperbolic systems under partial dissipation which is localized in suitable subsets of the domain. More precisely, we recover the classical decay rates of partially dissipative systems…
We analyze the exponential stability of distributed parameter systems. The system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients. We approximate the coefficients by…
In this paper we consider a stabilization problem for the abstract-wave equation with delay. We prove an exponential stability result for appropriate damping coefficient. The proof of the main result is based on a frequency-domain approach.
We consider $N$ Euler-Bernoulli beams and $N$ strings alternatively connected to one another and forming a particular network which is a chain beginning with a string. We study two stabilization problems on the same network and the spectrum…
In the present paper, we are concerned with the semilinear viscoelastic wave equation subject to a locally distributed dissipative effect of Kelvin-Voigt type, posed on a bounded domain with smooth boundary. We begin with an auxiliary…
In this paper we study time semi-discrete approximations of a class of polynomially stable infinite dimensional systems modeling the damped vibrations. We prove that adding a suitable numerical viscosity term in the numerical scheme, one…
In this paper, we give positive answer to the open question raised in [E. Zuazua, Exponential decay for the semilinear wave equation with localized damping in unbounded domains. J. Math. Pures Appl., 70 (1991) 513--529] on the exponential…
We study the large time behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We show that if the damping is effective, then the solution is asymptotically expanded in terms of solutions of…