# American Institute of Mathematical Sciences

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

## On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry

 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.
Citation: J. Földes, Peter Poláčik. On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry. Discrete & Continuous Dynamical Systems, 2009, 25 (1) : 133-157. doi: 10.3934/dcds.2009.25.133
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