On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry
J. Földes - School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States (email)
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.
Keywords: Parabolic cooperative
systems, positive solutions, asymptotic symmetry, Harnack
Received: August 2007; Revised: December 2007; Published: June 2009.
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