Transition fronts of time periodic bistable reaction–diffusion equations in R^N

This paper is concerned with the existence and qualitative properties of transition fronts for time periodic bistable reaction–diffusion equations in R^N. We first show that any almost-planar transition front is actually planar, regardless of the number of transition layers. Then we prove that all transition fronts admit a global mean speed γ and it holds γ=|c|, where c is the speed of the planar traveling front. Finally we establish the existence of a transition front in R^N that is not a standard traveling front. Such a front behaves like three moving time periodic planar fronts as time goes to −∞ and like a time periodic V-shaped traveling front as time goes to ∞.