Semi-wave and spreading speed for a nonlocal diffusive Fisher-KPP model with free boundaries in time periodic environment.

We consider a nonlocal diffusive Fisher-KPP model with free boun-daries in time periodic environment. When the growth term is Logistic type, Zhang et al. [DCDS-B 2021] proved that this model admits a unique global solution and its long time behavior is governed by a spreading-vanishing dichotomy. However, when spreading happens, the spreading speed estimates for such free boundary problems remain unsolved. In this paper, we answer this question. By solving a corresponding time-periodic semi-wave problem, we obtain a threshold condition on the kernel function such that the spreading grows linearly in time, and provide a sharp estimate for the spreading speed; when the threshold condition is not satisfied, we observe an accelerating spreading phenomenon. [ABSTRACT FROM AUTHOR]