Curved fronts of bistable reaction-diffusion equations in spatially periodic media: $N\ge 2$

Abstract

This paper is concerned with curved fronts of bistable reaction-diffusion equations in spatially periodic media for dimensions $N\geq 2$. The curved fronts concerned are transition fronts connecting $0$ and $1$. Under a priori assumption that there exist moving pulsating fronts in every direction, we show the existence of polytope-like curved fronts with $0$-zone being a polytope and $1$-zone being the complementary set. By reversing some conditions, we also show the existence of curved fronts with reversed $0$-zone and $1$-zone. Furthermore, the curved fronts constructed by us are proved to be unique and asymptotic stable.