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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

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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