Exponential Decay for the Solution of Semilinear Viscoelastic Wave Equations with Localized Damping

Date

2002-05-22

Authors

Cavalcanti, Marcelo M.
Domingos Cavalcanti, V. N.
Soriano, Juan A.

Journal Title

Journal ISSN

Volume Title

Publisher

Southwest Texas State University, Department of Mathematics

Abstract

In this paper we obtain an exponential rate of decay for the solution of the viscoelastic nonlinear wave equation utt - Δu + ƒ(x, t, u) + ∫t0 g(t - T) Δu(T) dT + α(x)ut = 0 in Ω x (0,∞). Here the damping term a(x)ut may be null for some part of the domain Ω. By assuming that the kernel g in the memory term decays exponentially, the damping effect allows us to avoid compactness arguments and and to reduce number of the energy estimates considered in the prior literature. We construct a suitable Liapunov functional and make use of the perturbed energy method.

Description

Keywords

Semilinear wave equation, Memory, Localized damping

Citation

Cavalcanti, M. M., Domingos Cavalcanti, V. N., & Soriano, J. A. (2002). Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping. <i>Electronic Journal of Differential Equations, 2002</i>(44), pp. 1-14.

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Attribution 4.0 International

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