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October 2011 Some examples causing energy growth for solutions to wave equations
Yuta Wakasugi
Proc. Japan Acad. Ser. A Math. Sci. 87(8): 136-141 (October 2011). DOI: 10.3792/pjaa.87.136

Abstract

In this paper we study energy growth for solutions to wave equations. We prove that there exist compact in space perturbations of the wave equation $\partial_{t}^{2}u-\triangle u=0$ such that the energy of solution grows at the rate $\exp((1+t)^{\alpha})$ for any $\alpha \geq 0$.

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Yuta Wakasugi. "Some examples causing energy growth for solutions to wave equations." Proc. Japan Acad. Ser. A Math. Sci. 87 (8) 136 - 141, October 2011. https://doi.org/10.3792/pjaa.87.136

Information

Published: October 2011
First available in Project Euclid: 3 October 2011

zbMATH: 1235.35188
MathSciNet: MR2843094
Digital Object Identifier: 10.3792/pjaa.87.136

Subjects:
Primary: 35L05 , 35L15

Keywords: compact in space perturbation , energy growth , wave equation

Rights: Copyright © 2011 The Japan Academy

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Vol.87 • No. 8 • October 2011
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