Existence of pyramidal traveling fronts to the buffered bistable systems in $\mathbb{R}^3$

Abstract

This paper studies the pyramidal calcium concentration waves for buffered bistable systems in $\mathbb{R}^3$. We show the existence of three-dimensional pyramidal traveling fronts by using the fixed point theory and the super-subsolution method combined with the comparison principle. Our result implies that multiple immobile buffers (where all buffers do not diffuse) do not affect the existence of pyramidal calcium concentration waves.