Nonplanar Traveling Fronts Of The Buffered Bistable System

The buffered bistable system is a type of classical biological model,which formulates functions of buffers in wave propagation.By studying traveling waves and nonplanar traveling fronts of this system,we can illustrate and predict a series of biological phenomena within and between cells.Therefore,it has been widely investigated in recent decades.But,compared to planar traveling waves which are relatively abundant,theoretical studies of nonplanar traveling fronts are still lacked.In this paper,for the first time,it is rigorously proved by mathematical theory that multiple stationary buffers(buffers do not diffuse)cannot prevent the existence of a stable V-shaped waves of calcium observed in the experiment.By constructing a series of proper supersolutions and subsolutions and then applying the comparison principle,we establish the existence of V-shaped waves and study the stability under the condition that the initial perturbation is not less than zero and decays to zero at infinity.