Electron. J. Diff. Eqns., Vol. 2007(2007), No. 131, pp. 1-13.

A nonlinear transmission problem with time dependent coefficients

Eugenio Cabanillas Lapa, Jaime E. Muñoz Rivera

In this article, we consider a nonlinear transmission problem for the wave equation with time dependent coefficients and linear internal damping. We prove the existence of a global solution and its exponential decay. The result is achieved by using the multiplier technique and suitable unique continuation theorem for the wave equation.

Submitted May 2, 2007. Published October 9, 2007.
Math Subject Classifications: 35B40, 35L70, 45K05.
Key Words: Transmission problem; time dependent coefficients; stability.

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Eugenio Cabanillas Lapa
Instituto de Investigación de Matemática
Facultad de Ciencias Matemáticas
Universidad Nacional Mayor de San Marcos, Lima, Peru
email: cleugenio@yahoo.com
Jaime E. Muñoz Rivera
Laboratorio Nacional de Computaçao Cientifica
Av. Getúlio Vargas, 333, 25651-070-Petropolis, Brazil
email: rivera@lncc.br

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