Stability of pyramidal traveling fronts in time-periodic reaction–diffusion equations with degenerate monostable and ignition nonlinearities

Abstract This article is concerned with the stability of time-periodic traveling fronts for reaction–diffusion equations with time-periodic degenerate monostable and ignition nonlinearities. Based on the existence of pyramidal traveling fronts established by Bu et al., we characterize the pyramidal traveling front as a combination of planar fronts on the lateral surfaces and establish some important estimates. Then, we show the asymptotic stability of pyramidal traveling fronts by using the sub-super solution method combined with the comparison principle.