Pyramidal traveling waves for a Belousov-Zhabotinskii system with obstacles

This paper is concerned with pyramidal traveling waves for Belousov-Zhabotinskii reaction-diffusion system in external domains $\Omega=\mathbb{R}^N\backslash K$ with a compact obstacle $K$ and aims to investigate the large time dynamics of an entire solution emanating from a pyramidal traveling wave. By constructing several super- and sub-solutions with desirable characteristics, some favorable properties of the pyramidal traveling wave are obtained. We show that by providing propagation completely of the entire solution, the pyramidal traveling wave will converge to the same shape of the pyramidal traveling wave after far behind the obstacle. AMS Subject Classification (2010): 35A18, 35B08, 35C07, 35K57