Asymptotic behaviour for wave equations with memory in a noncylindrical domains

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December 2003, 2(4): 511-520. doi: 10.3934/cpaa.2003.2.511

Asymptotic behaviour for wave equations with memory in a noncylindrical domains

Jorge Ferreira ^1, and Mauro De Lima Santos ^2,

1.	Departamento de Matemática-DMA, Universidade Estadual de Maringá-UEM, Campus Universitário, Av. Colombo, 5790-Zona 7, CEP 87020-900, Maringá-Pr., Brazil
2.	Departamento de Matemática, Universidade Federal do Pará, Campus Universitário do Guamá, Rua Augusto Corrêa 01, Cep 66075-110, Pará, Brazil

Received March 2003 Revised July 2003 Published October 2003

Abstract
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In this paper we prove the exponential decay as time goes to infinity of regular solutions of the problem for the wave equations with memory and weak damping

$u_{t t}-\Delta u+\int^t_0g(t-s)\Delta u(s)ds + \alpha u_{t}=0$ in $\hat Q$

where $\hat Q$ is a non cylindrical domains of $\mathbb R^{n+1}$ $(n\ge1)$ with the lateral boundary $\hat{\sum}$ and $\alpha$ is a positive constant.

Keywords: asymptotic behaviour., noncylindrical domain, Wave equations.

Mathematics Subject Classification: 35K55, 35F30, 34B1.

Citation: Jorge Ferreira, Mauro De Lima Santos. Asymptotic behaviour for wave equations with memory in a noncylindrical domains. Communications on Pure & Applied Analysis, 2003, 2 (4) : 511-520. doi: 10.3934/cpaa.2003.2.511

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