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February 2007 The wave equation for the $p$-Laplacian
Michael DREHER
Hokkaido Math. J. 36(1): 21-52 (February 2007). DOI: 10.14492/hokmj/1285766660

Abstract

We consider generalized wave equations for the $p$--Laplacian and prove the local in time existence of solutions to the Cauchy problem. We give an estimate of the life-span of the solution, and show by a generic counter-example that global in time solutions can not be expected.

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Michael DREHER. "The wave equation for the $p$-Laplacian." Hokkaido Math. J. 36 (1) 21 - 52, February 2007. https://doi.org/10.14492/hokmj/1285766660

Information

Published: February 2007
First available in Project Euclid: 29 September 2010

zbMATH: 1146.35060
MathSciNet: MR2309819
Digital Object Identifier: 10.14492/hokmj/1285766660

Subjects:
Primary: 35L80
Secondary: 35L70

Keywords: blow-up in finite time , local in time Sobolev solutions , Weakly hyperbolic equations

Rights: Copyright © 2007 Hokkaido University, Department of Mathematics

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Vol.36 • No. 1 • February 2007
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