Local energy decay for the damped Klein-Gordon equation in exterior domain

Abstract

We prove uniform local energy decay for the solution of the dissipative Klein–Gordon equation on an exterior domain under some geometric condition called “exterior geometric control”.

Keywords:

• Damped Klein–Gordon equation
• cut-off resolvent
• semi-classical measure

Acknowledgements

The author is grateful to the referee for useful comments and suggestions which led to an improvement of the paper. He would to thank his advisor professor Moez Khenissi for his invaluable help, encouragement and guidance. He also would like to thank professor Lassaad Aloui for helpful discussions.

Notes

No potential conflict of interest was reported by the author.