Competition in periodic media: II - Segregative limit of pulsating fronts and Unity is not Strength-type result

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:265

Article

Girardin, Leo¹  Nadin, Gregoire¹ 

[1] Univ Paris 06, CNRS UMR 7598, Lab Jacques Louis Lions, 4 Pl Jussieu, F-75005 Paris, France

关键词: Pulsating fronts;    Periodic media;    Competition-diffusion system;    Segregation;    Wave speed;    Free boundary;   

DOI  :  10.1016/j.jde.2018.02.026

来源: Elsevier

【 摘 要 】

This paper is concerned with the limit, as the interspecific competition rate goes to infinity, of pulsating front solutions in space-periodic media for a bistable two-species competition-diffusion Lotka-Volterra system. We distinguish two important cases: null asymptotic speed and non-null asymptotic speed. In the former case, we show the existence of a segregated stationary equilibrium. In the latter case, we are able to uniquely characterize the segregated pulsating front, and thus full convergence is proved. The segregated pulsating front solves an interesting free boundary problem. We also investigate the sign of the speed as a function of the parameters of the competitive system. We are able to determine it in full generality, with explicit conditions depending on the various parameters of the problem. In particular, if one species is sufficiently more motile or competitive than the other, then it is the invader. This is an extension of our previous work in space-homogeneous media. (c) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free