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2004 Non decay of the total energy for the wave equation with the dissipative term of spatial anisotropy
Mishio Kawashita, Hideo Nakazawa, Hideo Soga
Nagoya Math. J. 174: 115-126 (2004).

Abstract

We consider the behavior of the total energy for the wave equation with the dissipative term. When the dissipative term works well uniformly in every direction, several authors obtain uniform decay estimates of the total energy. On the other hand, if the dissipative term is small enough uniformly in every direction, it is known that there exists a solution whose total energy does not decay. We examine the case that the dissipative term vanishes only in a neighborhood of a half-line. We introduce a uniform decay property, which is a natural generalization of the uniform decay estimates, and show that this property does not hold in our case. We prove this by constructing asymptotic solutions supported in the place where the dissipative term vanishes.

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Mishio Kawashita. Hideo Nakazawa. Hideo Soga. "Non decay of the total energy for the wave equation with the dissipative term of spatial anisotropy." Nagoya Math. J. 174 115 - 126, 2004.

Information

Published: 2004
First available in Project Euclid: 27 April 2005

zbMATH: 1053.35076
MathSciNet: MR2066105

Subjects:
Primary: 35L15
Secondary: 35B40

Rights: Copyright © 2004 Editorial Board, Nagoya Mathematical Journal

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Vol.174 • 2004
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