Carleman estimates for second-order hyperbolic systems in anisotropic cases and applications. Part II: an inverse source problem

Abstract

In this paper, we consider Carleman-type estimate and consider an inverse problem for second order hyperbolic systems in an anisotropic case. In the previous Part I paper, we established a Carleman-type estimate for hyperbolic systems in which the coefficient matrices satisfy suitable conditions. We apply a Carleman estimate in the previous Part I paper to an inverse source problem for second-order hyperbolic systems in an anisotropic case and prove an estimate of the Hölder type.

Keywords:

• hyperbolic systems
• anisotropic cases
• inverse source problem

AMS Subject Classifications:

• 35L55
• 35R30
• 74E10

Acknowledgements

The author thanks Professor Masahiro Yamamoto (Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, Japan) for his valuable comments. The author also thanks anonymous referees for their valuable comments.

Notes

Project 11101391 supported by National Natural Science Foundation of China.