Stability estimate in determination of a coefficient in transmission wave equation by boundary observation

Abstract

In this paper, we study the global stability in determination of a coefficient in the transmission wave equation from data of the solution in a subboundary over a time interval. Providing regular initial data, we prove a hölder stability estimate in the inverse problem with a single measurement. Moreover, the exponent in the stability estimate depends on the regularity of initial data.

Keywords:

• Carleman estimates
• transmission wave equation
• inverse problem

AMS Subject Classifications:

• 35L20
• 35R30

Acknowledgements

The author thank the anonymous referee for very useful comments and insightful suggestions. The author is grateful to Professor M. Bellassoued for instructive discussions, for his useful remarks, and for his comments on this work.