Electron. J. Diff. Eqns., Vol. 2006(2006), No. 53, pp. 1-16.

Nonlinear transmission problem with a dissipative boundary condition of memory type

Doherty Andrade, Luci Harue Fatori, Jaime E. Munoz Rivera

We consider a differential equation that models a material consisting of two elastic components. One component is clamped while the other is in a viscoelastic fluid producing a dissipative mechanism on the boundary. So, we have a transmission problem with boundary damping condition of memory type. We prove the existence of a global solution and its uniformly decay to zero as time approaches infinity. More specifically, the solution decays exponentially provided the relaxation function decays exponentially.

Submitted November 10, 2005. Published April 28, 2006.
Math Subject Classifications: 35B40, 35L70.
Key Words: Wave equation; asymptotic behavior; memory.

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Doherty Andrade
Maringá State University, Departament of Mathematics
87020-900 - Maringá, Brazil
email: doherty@uem.br
  Luci H. Fatori
Londrina State University, Departament of Mathematics
86051-990 - Londrina, Brazil
email: lucifatori@uel.br
Jaime E. Muñoz Rivera
Laboratório Nacional de Computação Científica
Av. Getúlio Vargas, 333, 25651-070 - Petrópolis, Brazil
email: rivera@lncc.br

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