V -shaped fronts of the diffusion system with Belousov–Zhabotinskii reaction in exterior domains

This paper studies a Belousov–Zhabotinskii (B-Z for short) reaction-diffusion system in exterior domains Ω=RN\K, where K is a compact set in RN. First, we establish the existence of an entire solution originating from any transition waves in Ω. Next, we investigate the large time dynamics of an entire solution originating from a V-shaped front and show that the entire solution converges to the same V-shaped front after passing the obstacle, in the case of complete propagation. The key method of this paper is to combine the sub- and super-solutions method with the comparison principle, for which several well-characterized modified systems are constructed.