Wave equations with time-dependent dissipation II. Effective dissipation

This article is intended to present a construction of structural representations of solutions to the Cauchy problem for wave equations with time-dependent dissipation above scaling. These representations are used to give estimates of the solution and its derivatives based on L q ( R n ) , q ⩾ 2 . Th...

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Bibliographic Details
Published in:Journal of Differential Equations 2007, Vol.232 (1), p.74-103
Main Author: Wirth, Jens
Format: Article
Language:English
Subjects:
A-priori estimates
Diffusive structure
Effective dissipation
Wave equations
WKB representations
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Summary:This article is intended to present a construction of structural representations of solutions to the Cauchy problem for wave equations with time-dependent dissipation above scaling. These representations are used to give estimates of the solution and its derivatives based on L q ( R n ) , q ⩾ 2 . The article represents the second part within a series. In [Jens Wirth, Wave equations with time-dependent dissipation I. Non-effective dissipation, J. Differential Equations 222 (2) (2006) 487–514] weak dissipations below scaling were discussed.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2006.06.004