Optimal bounds and blow-up criteria for a semi-linear accretive wave equation

Abstract

In this paper we consider the semi-linear wave equation: $u_{tt}-\Delta u=u_t|u_t{|}^{p-1}$ in ${\mathbb{R}}^N$ where $1<p\le 1+\frac{2}{N-1}$ and $p<5$ if N=1, $p\ne 3$ if N=2. We give an energetic criteria and optimal lower bound for blowing up solutions of this equation.

arXiv commentWe withdraw this paper since a minor calculation error was made at the very beginning of the paper