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June 2012 Generalized energy conservation for Klein--Gordon type equations
Christiane Böhme, Fumihiko Hirosawa
Osaka J. Math. 49(2): 297-323 (June 2012).

Abstract

The aim of this paper is to derive energy estimates for solutions of the Cauchy problem for the Klein--Gordon type equation $u_{tt} - \bigtriangleup u + m(t)^{2} u = 0$. The coefficient $m$ is given by $m(t)^{2} = \lambda(t)^{2} + p(t)$ with a decreasing, smooth shape function $\lambda$ and an oscillating, smooth and bounded perturbation function $p$. We study under which assumptions for $\lambda$ and $p$ one can expect results about a generalization of energy conservation. The main theorems of this note deal with $m$ belonging to $C^{M}$, $M \ge 2$, and $m$ belonging to the Gevrey class $\gamma^{(s)}$, $s \ge 1$.

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Christiane Böhme. Fumihiko Hirosawa. "Generalized energy conservation for Klein--Gordon type equations." Osaka J. Math. 49 (2) 297 - 323, June 2012.

Information

Published: June 2012
First available in Project Euclid: 20 June 2012

zbMATH: 1250.35133
MathSciNet: MR2945750

Subjects:
Primary: 35B20 , 35B40 , 35L15

Rights: Copyright © 2012 Osaka University and Osaka City University, Departments of Mathematics

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Vol.49 • No. 2 • June 2012
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