ASYMPTOTIC BEHAVIOR OF ENTIRE SOLUTIONS TO REACTION-DIFFUSION EQUATIONS IN AN INFINITE STAR GRAPH

We deal with the bistable reaction-diffusion equation in an infinite star graph, which consists of several half-lines with a common end point. The aim of our study is to show the existence of front-like entire solutions together with the asymptotic behaviors as t -> +/-infinity and classify the entire solutions according to their behaviors, where an entire solution is meant by a classical solution defined for all t is an element of(-infinity,infinity). To this end, we give a condition under that the front propagation is blocked by the emergence of standing stationary solutions. The existence of an entire solution which propagates beyond the blocking is also shown.