Spreading in space-time periodic media governed by a monostable equation with free boundaries, Part 2: Spreading speed

Author(s)
Ding, Weiwei
Du, Yihong
Liang, Xing
Publication Date
2019
Abstract
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 [2]) 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.
Citation
Annales de l'Institut Henri Poincaré (C), Analyse Non Linéaire, 36(6), p. 1539-1573
ISSN
1873-1430
0294-1449
Link
Publisher
Elsevier BV
Title
Spreading in space-time periodic media governed by a monostable equation with free boundaries, Part 2: Spreading speed
Type of document
Journal Article
Entity Type
Publication

Files:

NameSizeformatDescriptionLink