On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry

J. Földes; Peter Poláčik

doi:10.3934/dcds.2009.25.133

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2009, Volume 25, Issue 1: 133-157. Doi: 10.3934/dcds.2009.25.133

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On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry

J. Földes^1, and
Peter Poláčik^1,

1.
School of Mathematics, University of Minnesota, Minneapolis, MN 55455

Received: July 31, 2007

Revised: November 30, 2007

Published: December 2008

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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.

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Mathematics Subject Classification: 35K50, 35B40, 35B45.

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