This is Part 2 of our work aimed at classifying the long-time behavior of the solution to a free boundary problem with monostable reaction term in space–time periodic media. In Part 1 (see ) we have established a theory on the existence and uniqueness of solutions to this free boundary problem with continuous initial functions, as well as a spreading-vanishing dichotomy. We are now able to develop the methods of Weinberger [15,16] and others [6–10] to prove the existence of asymptotic spreading speed when spreading happens, without knowing a priori the existence of the corresponding semi-wave solutions of the free boundary problem. This is a completely different approach from earlier works on the free boundary model, where the spreading speed is determined by firstly showing the existence of a corresponding semi-wave. Such a semi-wave appears difficult to obtain by the earlier approaches in the case of space–time periodic media considered in our work here.
Cite this article
Weiwei Ding, Yihong Du, Xing Liang, Spreading in space–time periodic media governed by a monostable equation with free boundaries, Part 2: Spreading speed. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 6, pp. 1539–1573DOI 10.1016/J.ANIHPC.2019.01.005