Global nonexistence results for a class of hyperbolic systems

Belkacem Said-Houari, Mokhtar Kirane

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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 [11] 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) [12] and Galaktionov and Pohozaev (2003) [11]. The advantage here is that our result applies to a wide variety of problems. © 2011 Elsevier Ltd. All rights reserved.
Original languageEnglish (US)
Pages (from-to)6130-6143
Number of pages14
JournalNonlinear Analysis: Theory, Methods & Applications
Volume74
Issue number17
DOIs
StatePublished - Dec 2011

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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