On a Kelvin--Voigt Viscoelastic Wave Equation with Strong Delay

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

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...

A Wave Equation with Discontinuous Time Delay

The influence of certain discontinuous delays on the behavior of the solutions of the wave equation is studied.

Frictional versus Viscoelastic Damping in a Semilinear Wave Equation

In this article we show exponential and polynomial decay rates for the partially viscoelastic nonlinear wave equation subject to a nonlinear and localized frictional damping. The equation that model this problem is given by utt − κ0∆u + ∫ t 0 div[a(x)g(t− s)∇u(s)] ds + f(u) + b(x)h(ut) = 0 in Ω× R, (0.1) where a, b are nonnegative functions, a ∈ C(Ω), b ∈ L∞(Ω), satisfying the assumption a(x) +...

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 ...