Global stability of critical-speed pulsating fronts for degenerate monostable reactions

Abstract

This paper is devoted to the global exponential stability of pulsating fronts for a kind of reaction–advection–diffusion equations with degenerate monostable nonlinearity in a periodic medium. We focus on the pulsating front with critical-speed, which is unique up to translation and decays exponentially when it approaches the unstable steady state 0. Based on the sub-super solution and the squeezing methods, we show that the solution will converge to a shift of the front exponentially in time when the general initial data decays faster than a positive exponential function at one end and has a positive lower bound at the other end.