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

Ding, Weiwei; Du, Yihong; Liang, Xing

doi:10.1016/j.anihpc.2019.01.005

Ding, Weiwei ^1,² ; Du, Yihong ¹ ; Liang, Xing ³

¹ School of Science and Technology, University of New England, Armidale, NSW 2351, Australia
² Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Tokyo 164-8525, Japan
³ School of Mathematical Sciences and Wu Wen-Tsun Key Laboratory of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, PR China

Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 6, pp. 1539-1573.

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Résumé

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.

MR Zbl

DOI : 10.1016/j.anihpc.2019.01.005

Classification : 35K20, 35R35, 35J60, 92B05
Mots-clés : Free boundary, Space–time periodic media, Monostable equation, Spreading speed

Affiliations des auteurs :

Ding, Weiwei ^{1, 2} ; Du, Yihong ¹ ; Liang, Xing ³

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     title = {Spreading in space{\textendash}time periodic media governed by a monostable equation with free boundaries, {Part} 2: {Spreading} speed},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1539--1573},
     publisher = {Elsevier},
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Ding, Weiwei; Du, Yihong; Liang, Xing. Spreading in space–time periodic media governed by a monostable equation with free boundaries, Part 2: Spreading speed. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 6, pp. 1539-1573. doi : 10.1016/j.anihpc.2019.01.005. http://www.numdam.org/articles/10.1016/j.anihpc.2019.01.005/

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