Curved fronts of bistable reaction-diffusion equations in spatially periodic media

TL;DR

This paper establishes the existence, uniqueness, and stability of curved traveling fronts in spatially periodic bistable reaction-diffusion equations, extending known results from homogeneous media to heterogeneous, periodic environments.

Contribution

It provides new sufficient and necessary conditions for curved front existence and constructs fronts with varying interfaces in periodic media.

Findings

Curved fronts exist under certain conditions in periodic media.

Curved fronts are proven to be unique and stable.

Construction of curved fronts with varying interfaces.

Abstract

In this paper, curved fronts are constructed for spatially periodic bistable reaction-diffusion equations under the a priori assumption that there exist pulsating fronts in every direction. Some sufficient and some necessary conditions of the existence of curved fronts are given. Furthermore, the curved front is proved to be unique and stable. Finally, a curved front with varying interfaces is also constructed. Despite the effect of the spatial heterogeneity, the result shows the existence of curved fronts for spatially periodic bistable reaction-diffusion equations which is known for the homogeneous case.