Uniqueness and stability in determining the speed of propagation of second-order hyperbolic equation with variable coefficients

Abstract

One of the basic inverse problems in an anisotropic media is the determination of coefficients in a bounded domain with a single measurement. We consider the problem of finding the coefficient of the second derivatives in a second-order hyperbolic equation with variable coefficients.

Under a weak regularity assumption and a geometrical condition on the metric, we prove the uniqueness in a multidimensional hyperbolic inverse problem with a single measurement. Moreover we show that our uniqueness results yield the Lipschitz stability estimate in L ² space for solution to the inverse problem under consideration.

Keywords:

• Inverse problems
• Boundary value problems
• AMS Subject Classification: 35L20

Acknowledgments

A part of this article was written while the author was visiting the Université de Versailles. The author would like thank Professor Robbiano for his kind invitation and hospitality, as well as for some useful discussions.

Notes

*E-mail: [email protected]

Additional information

Notes on contributors

Mourad Bellassoued *

*E-mail: [email protected]