Hokkaido Mathematical Journal

The wave equation for the $p$-Laplacian

Michael DREHER

Full-text: Open access

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.

Article information

Source
Hokkaido Math. J. Volume 36, Number 1 (2007), 21-52.

Dates
First available in Project Euclid: 29 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1285766660

Digital Object Identifier
doi:10.14492/hokmj/1285766660

Mathematical Reviews number (MathSciNet)
MR2309819

Zentralblatt MATH identifier
1146.35060

Subjects
Primary: 35L80: Degenerate hyperbolic equations
Secondary: 35L70: Nonlinear second-order hyperbolic equations

Keywords
local in time Sobolev solutions blow-up in finite time weakly hyperbolic equations

Citation

DREHER, Michael. The wave equation for the $p$-Laplacian. Hokkaido Math. J. 36 (2007), no. 1, 21--52. doi:10.14492/hokmj/1285766660. https://projecteuclid.org/euclid.hokmj/1285766660.


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