Local energy decay for the wave equation with a nonlinear time-dependent damping

Abstract

This article addresses a wave equation on a exterior domain in ℝ ^d (d odd) with nonlinear time-dependent dissipation. Under a microlocal geometric condition we prove that the decay rates of the local energy functional are obtained by solving a nonlinear non-autonomous differential equation

Keywords:

• wave equation
• nonlinear dissipation
• internal damping
• decay rates
• time-dependent dissipation

AMS Subject Classifications::

• 35L05
• 35B40

Acknowledgements

The authors are very grateful to the anonymous referees for their helpful comments and suggestions, that improved the manuscript. This article has been supported by deanship of scientific research of Dammam University under the reference 2012045.