V-shaped transition fronts of monotone bistable reaction-diffusion systems in exterior domains

TL;DR

This paper studies V-shaped transition fronts in a bistable reaction-diffusion system within exterior domains, demonstrating existence, monotonicity, and asymptotic profile recovery of these fronts under certain conditions.

Contribution

It constructs and analyzes V-shaped transition fronts in exterior domains, showing their existence, monotonicity, and asymptotic behavior in bistable reaction-diffusion systems.

Findings

Existence of V-shaped transition fronts established.

Fronts recover V-shape asymptotically after passing obstacles.

Global mean speed matches planar wave speed.

Abstract

This paper investigates the propagation phenomena of a monotone bistable reaction-diffusion system in an exterior domain of R2. By constructing suitable sub- and supersolutions, we establish the existence and monotonicity of an entire solution originating from a V-shaped traveling front. It is further shown that, under the complete propagation condition, this entire solution eventually recovers its V-shaped profile as time tends to infty after passing the obstacle. In particular, we show that the entire solution is a V-shaped transition front whose global mean speed coincides with the planar wave speed.