2016/11/07 by Weiwei Ding, Yihong Du, Ding, Weiwei +3
Engineering · Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations #math.AP
paper · pdf · doi:10.48550/arxiv.1611.01908
arxiv created 2016/11/07 · openalex publication_date 2016/11/07 · arxiv updated 2016/11/08 · openalex created_date 2016/11/30 · openalex updated_date 2026/07/28
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 \citeddl) 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 \citew1, w2 and others \citefyz,lyz,lz1,lz2,lui 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.