Uniqueness and global stability of V-shaped fronts for the buffered bistable system in R2. (April 2023) - Jia, Fu-Jie; Bu, Zhen-Hui; Ma, Zhuo
Abstract: This paper is devoted to V-shaped calcium concentration waves of the buffered bistable system in R 2 . We prove that multiple immobile buffers (where all buffers do not diffuse) do not affect the global asymptotic stability and uniqueness of V-shaped calcium concentration waves. The existence of such curved fronts has been proved in our previous work (Jia et al., 2022). However, the study of its stability is difficult since the buffers do not diffuse. We first apply the sliding method to construct a crucial sub-solution. Then, based on the super- and sub-solution method, and comparison principle, we achieve the global asymptotic stability of the V-shaped fronts.