Stability of the wave equation with localized Kelvin-Voigt damping and boundary delay feedback

Stability of an abstract-wave equation with delay and a Kelvin-Voigt damping

Stability of a Nonlinear Axially Moving String with the Kelvin-Voigt Damping

In this paper, a nonlinear axially moving string with the Kelvin-Voigt damping is considered. It is proved that the string is stable, i.e., its transversal displacement converges to zero when the axial speed of the string is less than a certain critical value. The proof is established by showing that a Lyapunov function corresponding to the string decays to zero exponentially. It is also shown ...

The Lack of Exponential Stability in Certain Transmission Problems with Localized Kelvin-Voigt Dissipation

Abstract. In this paper we consider the transmission problem of a material composed of three components; one of them is a Kelvin–Voigt viscoelastic material, the second is an elastic material (no dissipation), and the third is an elastic material inserted with a frictional damping mechanism. The main result of this paper is that the rate of decay will depend on the position of each component. W...

Transmission Problems in (Thermo)Viscoelasticity with Kelvin-Voigt Damping: Nonexponential, Strong, and Polynomial Stability

We investigate transmission problems between a (thermo-)viscoelastic system with Kelvin-Voigt damping, and a purely elastic system. It is shown that neither the elastic damping by Kelvin-Voigt mechanisms nor the dissipative effect of the temperature in one material can assure the exponential stability of the total system when it is coupled through transmission to a purely elastic system. The ap...

Exponential Stability of the System of Transmission of the Wave Equation with a Delay Term in the Boundary Feedback

We consider a system of transmission of the wave equation with Neumann feedback control that contains a delay term and that acts on the exterior boundary. First, we prove under some assumptions that the closed-loop system generates a C0−semigroup of contractions on an appropriate Hilbert space. Then, under further assumptions, we show that the closed-loop system is exponentially stable. To esta...