Global existence and decay of solutions of a nonlinear system of wave equations

Abstract

This work is concerned with a system of two wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we show that our problem has a unique local solution. Also, we prove that, for some restrictions on the initial data, the rate of decay of the total energy is exponential or polynomial depending on the exponents of the damping terms in both equations.

Keywords:

• decay
• energy
• source
• damping

AMS Subject Classifications::

• 35L05
• 35L20
• 58G16

Acknowledgements

The author was partially supported by MIRA 2007 project of the Région Rhone-Alpes. This author wishes to thank Université de Savoie of Chambéry for its kind hospitality. Moreover, the author wishes to thank the referees for their useful remarks and their careful reading of the proofs presented in this article.