Electron. J. Diff. Eqns., Vol. 2007(2007), No. 60, pp. 1-10.

Transmission problem for waves with frictional damping

Waldemar D. Bastos, Carlos A. Raposo

In this paper we consider the transmission problem, in one space dimension, for linear dissipative waves with frictional damping. We study the wave propagation in a medium with a component with attrition and another simply elastic. We show that for this type of material, the dissipation produced by the frictional part is strong enough to produce exponential decay of the solution, no matter how small is its size.

Submitted June 23, 2006. Published April 22, 2007.
Math Subject Classifications: 35B35, 35B40, 35L05, 35L20.
Key Words: Exponential stability; dissipative system; transmission problem.

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Waldemar D. Bastos
Universidade Estadual Paulista - UNESP
Departamento de Matemática
15054-000 - São José do Rio Preto - SP, Brazil
email: waldemar@ibilce.unesp.br
Carlos A. Raposo
Universidade Federal de São João del-Rei - UFSJ
Departamento de Matemática
36300-000 - São João del-Rei, MG, Brazil
email: raposo@ufsj.edu.br

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