Qualitative properties of pulsating fronts for reaction-advection-diffusion equations in periodic excitable media

In this paper, we study the pulsating fronts of reaction-advection-diffusion equations with two types of nonlinear term in periodic excitable media. Firstly, for the case with combustion nonlinearity, the unique front is proved to decay exponentially when it approaches the unstable limiting state. Secondly, for the degenerate monostable type nonlinearity, it is shown that the front with critical speed is unique, monotone and decays exponentially at negative end, while the fronts of noncritical speeds decay to zero non-exponentially. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper studies the pulsating fronts of reaction-advection-diffusion equations with two types of nonlinear terms in periodic excitable media. It is shown that for the case with combustion nonlinearity, the unique front decays exponentially when approaching the unstable limiting state, while for the degenerate monostable type nonlinearity, the front with critical speed is unique, monotone, and decays exponentially at the negative end. Noncritical speed fronts decay to zero non-exponentially.