Asymptotic stability of traveling wave fronts in the buffered bistable system

In this paper, we study a model which describes the propagation of increased calcium concentration wave front in excitable systems with the diffusing species being buffered. Our goal is to prove the global exponential stability of the unique traveling wave front. Comparing with the unbuffered system, we conclude that multiple stationary buffers (buffers do not diffuse) cannot prevent the existence of a global asymptotic stable traveling wave front, or cannot eliminate propagated waves in the buffered bistable equation. Concerning the method of the proof, we will present a method in which only the comparison principle and suitably constructed supersolutions (subsolutions) are involved. The feature of the method is to avoid calculating the spectrum of the associated linear operator.