Uniform decay estimates for the semi-linear wave equation with locally distributed mixed-type damping via arbitrary local viscoelastic versus frictional dissipative effects

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) +...

Frictional versus viscoelastic damping for Timoshenko-type systems

In this paper we consider the following Timoshenko system φtt − (φx + ψ)x = 0, (0, 1)× (0,+∞) ψtt−ψxx + ∫ t 0 g(t−τ)(a(x)ψx(τ))xdτ +φx +ψ+b(x)h(ψt) = 0, (0, 1)×(0,∞) with Dirichlet boundary conditions where a, b, g, and h are specific functions. We establish an exponential and polynomial decay results. This result improves and generalizes some existing results in the literature.

Uniform Stabilization of the Wave Equation on Compact Surfaces and Locally Distributed Damping

This paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping, described by utt −∆Mu+ a(x) g(ut) = 0 on M× ]0,∞[ , where M ⊂ R is a smooth (of class C) oriented embedded compact surface without boundary, such that M = M0 ∪M1, where M1 := {x ∈ M;m(x) · ν(x) > 0} and M0 = M\M1. Here, m(x) := x − x, (x ∈ R fixed) and ν is the exterior unit normal v...

Decay Estimates for the Wave Equation with Potential*

Optimal decay estimates for the general solution to a class of semi-linear dissipative hyperbolic equations

We consider a class of semi-linear dissipative hyperbolic equations in which the operator associated to the linear part has a nontrivial kernel. Under appropriate assumptions on the nonlinear term, we prove that all solutions decay to 0, as t → +∞, at least as fast as a suitable negative power of t. Moreover, we prove that this decay rate is optimal in the sense that there exists a nonempty ope...