V-shaped transition fronts of monotone bistable reaction-diffusion systems in exterior domains
Analysis of PDEs
2026-03-25 v1
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.
Keywords
Cite
@article{arxiv.2603.22896,
title = {V-shaped transition fronts of monotone bistable reaction-diffusion systems in exterior domains},
author = {Yang-Yang Yan and Wei-Jie Sheng},
journal= {arXiv preprint arXiv:2603.22896},
year = {2026}
}