A degenerate parabolic system with self-diffusion for a mutualistic model in ecology

Abstract

This paper deals with the behavior of positive solution for a degenerate parabolic system with homogeneous Dirichlet boundary conditions describing a cooperating two-species Lotka–Volterra model. The local existence and uniqueness of a classical solution are given. Some comparison principles and positivity lemmas are also presented. Further, we show that the solution is global if the intra-specific competitions of the species are strong, whereas the solution may blow up if the intra-specific competitions are weak.