ENTIRE SOLUTIONS OF BISTABLE REACTION-DIFFUSION SYSTEMS IN UNBOUNDED DOMAIN WITH MULTIPLE CYLINDRICAL BRANCHES

This paper is concerned with bistable reaction-diffusion systems in unbounded domains with multiple cylindrical branches. We first prove the existence of the entire solution u(t,x) emanating from planar fronts in some branches. Then, under the assumption that the propagation of u(t,x) is complete, we prove that u(t,x) converges to planar fronts in the other branches as t ->+infinity. Finally, we give some sufficient conditions such that the entire solution propagates completely.