This paper is devoted to a classical biological system for calcium buffering with bistable nonlinearity in exterior domains \(\Omega =\mathbb {R}^N\setminus K\) , where K denotes an obstacle and is a compact subset of \(\mathbb {R}^N\) . Our goal is to prove that multiple mobile buffers (all buffers do diffuse) cannot eliminate propagation phenomena of a calcium planar traveling front in \(\Omega \) . These phenomena mean that the calcium planar traveling front can gradually recover its profile and continue to propagate in the same direction after being disturbed by the obstacle K. We first prove that the buffered bistable system has an entire solution originating from a planar traveling front in \(\Omega \) . Using the high-dimensional stability of the planar traveling front, we further prove that the entire solution will gradually recover to the same planar traveling front after passing the obstacle K by providing the complete propagation of the entire solution.
