Related papers: Stabilization for vibrating plate with singular st…

We study a class of elastic systems described by a (hyperbolic) partial differential equation. Our working example is the equation of a vibrating string subject to linear disturbance. The main goal is to establish conditions for…

A system of partial differential equations describing the spatial oscillations of an Euler-Bernoulli beam with a tip mass is considered. The linear system considered is actuated by two independent controls and separated into a pair of…

We investigate the stability of a one-dimensional wave equation with non smooth localized internal viscoelastic damping of Kelvin-Voigt type and with boundary or localized internal delay feedback. The main novelty in this paper is that the…

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…

We investigate the numerical approximation to the Euler-Bernoulli (E-B) beams and plates with nonlinear nonlocal strong damping, which describes the damped mechanical behavior of beams and plates in real applications. We discretize the…

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 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.

Stochastic flexural vibrations of small-scale Bernoulli-Euler beams with external damping are investigated by stress-driven nonlocal mechanics. Damping effects are simulated considering viscous interactions between beam and surrounding…

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…

The dynamics of a (nonlinear) Berger plate in the absence of rotational inertia are considered with inhomogenous boundary conditions. In our analysis, we consider boundary damping in two scenarios: (i) free plate boundary conditions, or…

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…

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 give a necessary and sufficient condition, of geometric type, for the uniform decay of energy of solutions of the linear system of magnetoelasticity in a bounded domain with smooth boundary. A Dirichlet-type boundary condition is…

In this paper, we consider a wave equation with strong damping and logarithmic nonlinearity. This paper aims to study the local and global existence, uniqueness and the uniform energy decay rate of a weak solution under some sufficient…

We investigate a two-dimensional transmission model consisting of a wave equation and a Kirchhoff plate equation with dynamical boundary controls under geometric conditions. The two equations are coupled through transmission conditions…

In this paper, we investigate the energy decay of the solution to a viscoelastic wave equation with variable exponents logarithmic nonlinearity and weak damping in a bounded domain. We establish an explicit general decay result under mild…

We cope with a free boundary fluid-structure interaction model. In the model, the viscous incompressible fluid interacts with elastic body via the common boundary. The motion of the fluid is governed by Navier-Stokes equations while the…

We consider a free boundary problem modeling electrostatic microelectromechanical systems. The model consists of a fourth-order damped wave equation for the elastic plate displacement which is coupled to an elliptic equation for 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…

In this work, we consider a system of two wave equations coupled by velocities in one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling…