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

Mikko Salo

doi:10.3934/ipi.2007.1.537

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2007, Volume 1, Issue 3: 537-556. Doi: 10.3934/ipi.2007.1.537

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

Mikko Salo^1,

1.
Department of Mathematics and Statistics / RNI, University of Helsinki, P.O. Box 68, 00014 Helsinki

Received: November 2006

Published: August 2007

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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.

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Mathematics Subject Classification: Primary: 35L05, 35A17, 35B35, 35R30.

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