Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 53, pp. 1-5.
Title: Blow up of solutions to semilinear wave equations
Author: Mohammed Guedda (Univ. de Picardie Jules Verne, France)
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 > 1$, $(N-1)m < N+1$, 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.