## Hokkaido Mathematical Journal

### The wave equation for the $p$-Laplacian

Michael DREHER

#### 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

http://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

#### Citation

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