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.
Rights
Attribution 4.0 International