Existence of steady-state solutions for a class of competing systems with cross-diffusion and self-diffusion

Abstract

We focus on a system of two competing species with cross-diffusion and self-diffusion. By constructing an appropriate auxiliary function, we derive the sufficient conditions such that there are no coexisting steady-state solutions to the model. It is worth noting that the auxiliary function constructed above is applicable to Dirichlet, Neumann and Robin boundary conditions.

Keywords

• cross-diffusion
• self-diffusion
• steady-state solution
• maximum principle