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February  2009, 25(1): 133-157. doi: 10.3934/dcds.2009.25.133

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, United States

Received  August 2007 Revised  December 2007 Published  June 2009

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.
Keywords: positive solutions, Harnack inequality., asymptotic symmetry, Parabolic cooperative systems.
Mathematics Subject Classification: 35K50, 35B40, 35B4.
Citation: J. Földes, Peter Poláčik. On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 133-157. doi: 10.3934/dcds.2009.25.133
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