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

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...

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Bibliographic Details
Published in:Electronic journal of differential equations 2001-11, Vol.2001 (73), p.1-18
Main Author: Mauro de Lima Santos
Format: Article
Language:English
Subjects:
asymptotic behavior
Wave equations
Online Access:Get full text
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Summary: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.
ISSN:1072-6691