Transition fronts of combustion reaction–diffusion equations around an obstacle

This paper is concerned with transition fronts and their propagation speeds of combustion reaction–diffusion equations around an obstacle. Firstly, we establish the existence of a transition front emanating from a V-shaped traveling front by constructing appropriate sub- and supersolutions. Then we show that the transition front eventually recovers to the same V-shaped traveling front as time goes \(\infty \) $\infty$ under the complete propagation condition. Finally, we prove that in exterior domains, any transition front has a unique global mean speed and any transition front connecting 0 and 1 propagates completely.