On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry (Q841366)

The authors consider fully nonlinear weakly coupled systems of parabolic equations on a bounded reflectionally symmetric domain. By assuming that the system is cooperative and that the system satisfies suitable symmetry conditions, they prove the asymptotic symmetry of positive bounded solutions. The authors extend classical Harnack estimates in this context, and by means of this powerful tool, they use the method of moving hyperplane in the case of cooperative systems.