Lipschitz stability of an inverse problem for an acoustic equation

Abstract

An inverse problem of the determination of the coefficient p(x) in the equation is considered. The main difficulty here as compared with the previous results is that the function p(x) is involved together with its derivatives. A Lipschitz stability estimate is obtained using the method of Carleman estimates.

Keywords:

• Inverse problem
• Hyperbolic equation
• Carleman estimate
• Lipschitz stability
• Mathematical Subject Classification 2000: 35R30
• 35R25
• 35B60

Acknowledgments

The work of M.V. Klibanov was supported in part by a grant provided by the University of North Carolina at Charlotte. The work of M. Yamamoto was supported in part by Grants 15340027 and 15654015 from the Japan Society for the Promotion of Sciences.