Existence of non-constant stable equilibria in competition-diffusion equations
This paper studies two competing species described by the Lotka-Volterra type reaction-diffusion equations. It considers the coexistence problem in domains which are non-convex, but not necessarily dumbbell-shaped. By using maximum principle, it proves existence of a stable non-constant stationary solution if the curvature of a boundary and the magnitude of competition-diffusion are well-balanced.
scientific article; zbMATH DE number 408767