Stability of traveling waves with algebraic decaying in time-periodic diffusion equations

This paper deals with the asymptotic stability of traveling waves with non-critical speeds in a class of time-periodic diffusion equations with degenerate monostable nonlinearities. The algebraically decaying rates of monotone increasing traveling waves with non-critical speeds are established. Based on the asymptotic behaviors of traveling waves and fundamental solution of heat equation, we show that the faster monotone increasing traveling waves are globally asymptotically stable in an algebraically weighted space.