Curved Fronts of Bistable Reaction-Diffusion Equations in Spatially Periodic Media

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.

Automated summary

This study constructs curved fronts for spatially periodic bistable reaction-diffusion equations, assuming the existence of pulsating fronts in every direction, and provides both sufficient and necessary conditions for their existence. It is shown that the curved front is unique and stable, and a curved front with varying interfaces is also constructed. Despite spatial heterogeneity, the study demonstrates the existence of curved fronts, extending previous knowledge from the homogeneous case.