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Rendiconti del Circolo Matematico di Palermo

, Volume 48, Issue 1, pp 135–152 | Cite as

Localization of blow-up points for a parabolic system with a nonlinear boundary condition

  • D. F. Rial
  • J. D. Rossi
Article
  • 34 Downloads

Abstract

The authors localize the blow-up points of positive solutions of the systemu t u,v t v with conditions\(\frac{{\partial u}}{{\partial \eta }} = f(\upsilon ),\frac{{\partial \upsilon }}{{\partial \eta }} = g(u)\) at the boundary of a bounded smooth domain Θ under some restrictions off andg and the initial data (Δu 0, Δν0>c>0).

If Θ is a ball, the hypothesis on the initial data can be removed.

1991 Mathematics Subject Classification

35B35 35K55 35B05 

Key words and phrases

parabolic systems nonlinear boundary conditions blow up 

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Copyright information

© Springer 1999

Authors and Affiliations

  • D. F. Rial
    • 1
  • J. D. Rossi
    • 1
  1. 1.Departamento de Matemática Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos AiresBuenos AiresArgentina

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