On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry

J. Földes, P. Poláčik

Research output: Contribution to journalArticle

21 Scopus citations

Abstract

We consider fully nonlinear weakly coupled systems of parabolic equations on a bounded reflectionally symmetric domain. Assuming the system is cooperative we prove the asymptotic symmetry of positive bounded solutions. To facilitate an application of the method of moving hyperplanes, we derive Harnack type estimates for linear cooperative parabolic systems.

Original languageEnglish (US)
Pages (from-to)133-157
Number of pages25
JournalDiscrete and Continuous Dynamical Systems
Volume25
Issue number1
DOIs
StatePublished - Sep 1 2009

Keywords

  • Asymptotic symmetry
  • Harnack inequality
  • Parabolic cooperative systems
  • Positive solutions

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