Inverse Problems and Imaging (IPI)

Stability for solutions of wave equations with $C^{1,1}$ coefficients

Pages: 537 - 556, Volume 1, Issue 3, August 2007      doi:10.3934/ipi.2007.1.537

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Mikko Salo - Department of Mathematics and Statistics / RNI, University of Helsinki, P.O. Box 68, 00014 Helsinki, Finland (email)

Abstract: We consider the stable dependence of solutions to wave equations on metrics in $C^{1,1}$ class. The main result states that solutions depend uniformly continuously on the metric, when the Cauchy data is given in a range of Sobolev spaces. The proof is constructive and uses the wave packet approach to hyperbolic equations.

Keywords:  Wave equation, parametrix, stability.
Mathematics Subject Classification:  Primary: 35L05, 35A17, 35B35, 35R30.

Received: November 2006;      Available Online: July 2007.