Electron. J. Diff. Eqns., Vol. 2003(2003), No. 85, pp. 1-17.

Stability for a coupled system of wave equations of Kirchhoff type with nonlocal boundary conditions

Jorge Ferreira, Ducival C. Pereira, & Mauro L. Santos

We consider a coupled system of two nonlinear wave equations of Kirchhoff type with nonlocal boundary condition and we study the asymptotic behavior of the corresponding solutions. We prove that the energy decay at the same rate of decay of the relaxation functions, that is, the energy decays exponentially when the relaxation functions decay exponentially and polynomially when the relaxation functions decay polynomially.

Submitted April 2, 2003. Published August 14, 2003.
Math Subject Classifications: 34A34, 34M30, 35B05.
Key Words: Coupled system, wave equation, Galerkin method, asymptotic behavior, boundary value problem

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Jorge Ferreira
Departamento de Matematica-DMA
Universidade Estadual de Maringa-UEM
Av. Colombo, 5790-Zona 7
CEP 87020-900, Maringa-Pr., Brazil
email: jferreira@bs2.com.br
Ducival C. Pereira
Instituto de Estudos Superiores da Amazonia (IESAM)
Av. Gov. Jose Malcher 1148
CEP 66.055-260, Belem-Pa., Brazil
Faculdade Ideal(FACI), Rua dos Mundurucus
1427, CEP 66025-660, Belem-Pa., Brazil
email: ducival@aol.com
Mauro L. Santos
Departamento de Matematica, Universidade Federal do Para
Campus Universitario do Guama
Rua Augusto Correa 01, Cep 66075-110, Para, Brazil
email: ls@ufpa.br

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