Electron. J. Diff. Eqns., Vol. 2003(2003), No. 53, pp. 1-5.

Blow up of solutions to semilinear wave equations

Mohammed Guedda

Abstract:
This work shows the absence of global solutions to the equation
$$ u_{tt} = \Delta u + p^{-k}|u|^m,$$
in the Minkowski space $\mathbb{M}_0=\mathbb{R}\times\mathbb{R}^N$, where $ m greater than 1$, $(N-1)m less than N+1$, and $p $ is a conformal factor approaching 0 at infinity. Using a modification of the method of conformal compactification, we prove that any solution develops a singularity at a finite time.

Submitted November 15, 2002. Published May 3, 2003.
Math Subject Classifications: 35L70, 35B40, 35L15.
Key Words: Blow up, conformal compactification.

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Mohammed Guedda
Lamfa, CNRS UMR 6140
Universite de Picardie Jules Verne
Faculte de Mathematiques et d'Informatique
33, rue Saint-Leu 80039, Amiens, France
email: guedda@u-picardie.fr

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