Existence of non-constant stable equilibria in competition-diffusion equations. (English) Zbl 0823.35090
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.
Reviewer: C.Y.Chan (Lafayette)
MSC:
35K57 | Reaction-diffusion equations |
35K50 | Systems of parabolic equations, boundary value problems (MSC2000) |
92D25 | Population dynamics (general) |