Related papers: Stabilization of the weakly coupled wave-plate sys…
In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions related to the Kelvin-Voigt damping and a delay term acting on the boundary. If the weight of the delay term in the feedback is less than the…
We prove the global existence of small data solution in all space dimension for weakly coupled systems of semi-linear effectively damped wave, with different time-dependent coefficients in the dissipation terms. Moreover, nonlinearity terms…
The well-posedness for the supersonic solutions of the Euler-Poisson system for hydrodynamical model in semiconductor devices and plasmas is studied in this paper. We first reformulate the Euler-Poisson system in the supersonic region into…
We consider the simplest instabilities involving multiple unstable electrostatic plasma waves corresponding to four-dimensional systems of mode amplitude equations. In each case the coupled amplitude equations are derived up to third order…
We consider systems of parabolic linear equations, subject to Neumann boundary conditions on bounded domains in $\mathbb{R}^d$, that are coupled by a matrix-valued potential $V$, and investigate under which conditions each solution to such…
In this work, we present a numerical study of the wave stability of steady solitary waves over a localised topographic obstacle through the full Euler equations. There are two branches of the solutions: one from the perturbed uniform flow…
We consider a beam and a wave equations coupled on an elastic beam through transmission conditions. The damping which is locally distributed acts through one of the two equations only; its effect is transmitted to the other equation through…
In this paper, the vibration model of an elastic beam, governed by the damped Euler-Bernoulli equation $\rho(x)u_{tt}+\mu(x)u_{t}$$+\left(r(x)u_{xx}\right)_{xx}=0$, subject to the clamped boundary conditions $u(0,t)=u_x(0,t)=0$ at $x=0$,…
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…
Several newly developing hybrid imaging methods (e.g., those combining electrical impedance or optical imaging with acoustics) enable one to obtain some auxiliary interior information (usually some combination of the electrical conductivity…
We consider a recent plate model obtained as a scaled limit of the three dimensional Biot system of poro-elasticity. The result is a "2.5" dimensional linear system that couples traditional Euler-Bernoulli plate dynamics to a pressure…
In this work we determine the critical exponent for a weakly coupled system of semilinear wave equations with distinct scale-invariant lower order terms, when these terms make both equations in some sense parabolic-like. For the blow-up…
In this paper we consider a boundary stabilization problem for the wave equation with interior delay. We prove an exponential stability result under some Lions geometric condition. The proof of the main result is based on an identity with…
In this paper we are concerned with a initial boundary-value problem for a coupled system of two KdV equations, posed on the positive half line, under the effect of a localized damping term. The model arises when modeling the propagation of…
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…
Time-periodic weak solutions for a coupled hyperbolic-parabolic system are obtained. A linear heat and wave equation are considered on two respective $d$-dimensional spatial domains that share a common $(d-1)$-dimensional interface…
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 consider the total energy decay of the Cauchy problem for wave equations with a potential and an effective damping. We treat it in the whole one-dimensional Euclidean space. Fast energy decay is established with the help of potential.…
This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we…
We study a damped semi-linear wave equation in a bounded domain with smooth boundary. It is proved that any sufficiently smooth solution can be stabilised locally by a finite-dimensional feedback control supported by a given open subset…