Transition fronts of time periodic bistable reaction-diffusion equations around an obstacle

This paper is concerned with the existence and qualitative properties of transition fronts for time periodic bistable reaction-diffusion equations around an obstacle. We first prove that any transition front connecting 0 and 1 admits a global mean speed equal to the speed of the planar traveling front in Ω = ℝ^NK, where K is a compact set of ℝ^N. Then we show that there is an almost V-shaped traveling front in exterior domains under the complete propagation. Namely, there is an entire solution emanating from a time periodic V-shaped traveling, and passing the obstacle K after encountering the obstacle, then recovering to the same V-shaped front and continuing to propagate in the same direction.