Front propagation and blocking of time periodic bistable Lotka-Volterra competition-diffusion systems in cylindrical domains

Abstract

This paper is concerned with the propagation and blocking phenomena of time periodic bistable Lotka-Volterra competition-diffusion system in cylindrical domains. Firstly, we establish the existence of an entire solution emanating from a time periodic planar traveling front. Here the entire solution refers to a solution that is defined for all time and over the whole domain. Then we prove that the entire solution eventually converges to the same planar traveling front under the complete propagation condition when the domain is bilaterally straight. Finally, we give some sufficient conditions on the domain to ensure that the propagation of the entire solution is complete or be blocked.