On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry

Pages: 133 - 157, Volume 25, Issue 1, September 2009

doi:10.3934/dcds.2009.25.133       Abstract        Full Text (340.9K)       Related Articles

J. Földes - School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States (email)
Peter Poláčik - 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 inequality.
Mathematics Subject Classification:  35K50, 35B40, 35B45.

Received: August 2007;      Revised: December 2007;      Published: June 2009.