Propagation Dynamics for Time-Space Periodic and Partially Degenerate Reaction-Diffusion Systems with Time Delay

This paper is concerned with the propagation dynamics of a large class of time-space periodic and partially degenerate reaction-diffusion systems with time delay and monostable nonlinearity. In the cooperative case, based on the theory of principal eigenvalues for linear and partially degenerate systems with time delay, we establish the existence of spreading speeds and its coincidence with the minimal wave speed of time-space periodic traveling waves. In the noncooperative case, we introduce the definition of transition semi-waves and prove the existence and equality of the spreading speed and the minimal wave speed of transition semi-waves by constructing two auxiliary cooperative systems and using the comparison arguments. To overcome the difficulty arising from the lower regularity of solutions for partially degenerate systems, some new prior estimate is obtained for the existence of transition semi-waves.