Determining Spreading Speeds for Abstract Time-Periodic Monotone Semiflows

This paper is devoted to studying the spreading speed determinacy to an abstract time-periodic monotone semiflow, which is of monostable type with weak compactness and admits boundary equilibria in the phase space. The problem is challenging due to the existence of single spreading speed or multiple spreading speeds (fastest and slowest spreading speeds). We first study under what condition single spreading speed exists and establish necessary and sufficient conditions for linear and nonlinear selections of the spreading speed as well as the minimal wave speed of traveling wavefronts. In the case of multiple spreading speeds, the determinacy of each speed is further investigated based on the connection of wavefronts to the boundary equilibria. We apply our results to five time-periodic models: a delayed diffusive equation, a stream population model with a benthic zone, a nonlocal dispersal Lotka-Volterra model, and two cooperative systems.