Lipschitz stability in an inverse problem for a hyperbolic equation with a finite set of boundary data

Abstract

We consider an inverse problem of determining multiple coefficients of principal part of a scalar hyperbolic equation with Dirichlet boundary data. We prove the uniqueness and a Lipschitz stability estimate in the inverse problem with some observations on a suitable sub-boundary satisfying an appropriate geometrical condition. The key is a Carleman estimate for a hyperbolic operator with variable coefficients.

Keywords:

• Lipschitz stability
• inverse hyperbolic problems
• anisotropic media

Acknowledgements

The authors thank anonymous referees for invaluable comments.