Blow-Up at Space Infinity for Solutions of Cooperative Reaction-Diffusion Systems

• Shimojo Masahiko

  National Taiwan Normal University

• Umeda Noriaki

  The University of Tokyo

Abstract

We consider the Cauchy problem of cooperative reaction-diffusion systems with nonnegative initial data. Here we discuss the blow-up of a solution that occurs only at space infinity. We give sufficient conditions for such phenomena, and study an asymptotic behaviour at space infinity of the solutions at the blow-up time. In general, relatively little is proved on the locations of blow-up point for semilinear parabolic systems. However, our results can be applied to a large class of nonlinearity for some class of initial value. The reason of this is that, when the blow-up occurs only at space infinity, the effect of reaction is much stronger than that of diffusion, and the behaviour at space infinity is well approximated by the flat solution.

Journal

• Funkcialaj Ekvacioj

  Funkcialaj Ekvacioj 54 (2), 315-334, 2011

  Division of Functional Equations, The Mathematical Society of Japan

Keywords

• Blow-up at space infinity
• Cooperative reaction-diffusion systems

Details

• CRID: 1390282680090221312
• NII Article ID: 130000953651
• DOI: 10.1619/fesi.54.315
• ISSN: 05328721
• Web Site: http://www.jstage.jst.go.jp/article/fesi/54/2/54_2_315/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed