Electron. J. Diff. Eqns., Vol. 2001(2001), No. 73, pp. 1-11.

Asymptotic behavior of solutions to wave equations with a memory condition at the boundary

Mauro de Lima Santos

In this paper, we study the stability of solutions for wave equations whose boundary condition includes a integral that represents the memory effect. We show that the dissipation is strong enough to produce exponential decay of the solution, provided the relaxation function also decays exponentially. When the relaxation function decays polynomially, we show that the solution decays polynomially and with the same rate.

Submitted September 20, 2001. Published November 26, 2001.
Math Subject Classifications:39A11.
Key Words: Wave equations, asymptotic behavior.

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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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