Doherty Andrade, Luci Harue Fatori, Jaime E. Munoz Rivera
Abstract:
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 |
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| Luci H. Fatori Londrina State University, Departament of Mathematics 86051-990 - Londrina, Brazil email: lucifatori@uel.br | |
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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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