Generalised energy conservation law for wave equations with variable propagation speed

We investigate the long time behaviour of the L 2 -energy of solutions to wave equations with variable speed of propagation. The novelty of the approach is the combination of estimates for higher order derivatives of the coefficient with a stabilisation property.

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2009-10, Vol.358 (1), p.56-74
Main Authors: Hirosawa, Fumihiko, Wirth, Jens
Format: Article
Language:English
Subjects:
A priori estimates
Exact sciences and technology
Floquet theory
Generalised energy conservation law
Mathematical analysis
Mathematics
Partial differential equations
Sciences and techniques of general use
Wave equations
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Description
Summary:We investigate the long time behaviour of the L 2 -energy of solutions to wave equations with variable speed of propagation. The novelty of the approach is the combination of estimates for higher order derivatives of the coefficient with a stabilisation property.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2009.04.048