Non-simultaneous blow-up in a semilinear parabolic system

  • F. Quirós
  • J. D. Rossi

Abstract.

In this paper we study the possibility of non-simultaneous blow-up for positive solutions of a fully coupled system of two semilinear heat equations, \(u_t=\Delta u + u^{p_{11}} v^{p_{12}}, v_t=\Delta v + u^{p_{21}} v^{p_{22}}\). Under adequate hypotheses, we prove that if u blows up then v can fail to blow up if and only if \(p_{11} >1\) and \( p_{21} < p_{11}-1 \).

Key words. Blow-up, semilinear parabolic system. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Verlag, Basel, 2001

Authors and Affiliations

  • F. Quirós
    • 1
  • J. D. Rossi
    • 2
  1. 1.Departamento de Matemáticas, U. Autónoma de Madrid, 28049 Madrid, Spain, e-mail: fernando.quiros@uam.esES
  2. 2.Departamento de Matemática, F.C.E y N., UBA, 1428 Buenos Aires, Argentina, e-mail: jrossi@dm.uba.arAR

Personalised recommendations