Minimum domains for spatial patterns in a class of reaction diffusion equations

Abstract

We study a general class of scalar reaction/interacting population diffusion equations in two space dimensions: convective terms, due to wind, are included. We consider boundary conditions which include a measure of the hostility to the species in the exterior of the domain. The main point of the paper is to obtain estimates for the minimum domain size which can sustain spatially heterogeneous structures and indicate the type of patterns which could appear.