Our concern in this paper is to prove blow-up results to the non-autonomous nonlinear system of wave equations utt-Δu=a(t,x)| v|p,vtt-Δv=b(t,x)|u|q,t>0, x∈RN in any space dimension. We show that a curve F̃(p,q)=0 depending on the space dimension, on the exponents p,q and on the behavior of the functions a(t,x) and b(t,x) exists, such that all nontrivial solutions to the above system blow-up in a finite time whenever F̃(p,q)>0. Our method of proof uses some estimates developed by Galaktionov and Pohozaev in  for a single non-autonomous wave equation enabling us to obtain a system of ordinary differential inequalities from which the desired result is derived. Our result generalizes some important results such as the ones in Del Santo et al. (1996)  and Galaktionov and Pohozaev (2003) . The advantage here is that our result applies to a wide variety of problems. © 2011 Elsevier Ltd. All rights reserved.
|Original language||English (US)|
|Number of pages||14|
|Journal||Nonlinear Analysis: Theory, Methods & Applications|
|State||Published - Dec 2011|
ASJC Scopus subject areas
- Applied Mathematics