Electron. J. Diff. Eqns., Vol. 2002(2002), No. 38, pp. 1-17.

Decay rates for solutions of a system of wave equations with memory

Mauro de Lima Santos

The purpose of this article is to study the asymptotic behavior of the solutions to a coupled system of wave equations having integral convolutions as memory terms. We prove that when the kernels of the convolutions decay exponentially, the first and second order energy of the solutions decay exponentially. Also we show that when the kernels decay polynomially, these energies decay polynomially.

Submitted March 18, 2002. Published May 6, 2002.
Math Subject Classifications: 35B40.
Key Words: Asymptotic behavior, wave equation.

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Mauro L. Santos
Departamento de Matematica,
Universidade Federal do Para
Campus Universitario do Guama
Rua Augusto Correa 01, Cep 66075-110,
Para, Brazil
e-mail: ls@ufpa.br

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