Traveling waves for reaction-diffusion PDE coupled to difference equation with nonlocal dispersal term and time delay

被引：3

作者：

Adimy, Mostafa ^{[1
]}

Chekroun, Abdennasser ^{[2
]}

Kazmierczak, Bogdan ^{[3
]}

机构：

[1] Univ Lyon 1, Inst Camille Jordan, CNRS UMR 5208, Inria, F-69200 Villeurbanne, France

[2] Univ Tlemcen, Lab Anal Nonlineaire & Math Appl, Tilimsen 13000, Algeria

[3] Polish Acad Sci, Inst Fundamental Technol Res, Pawinskiego 5B, PL-02106 Warsaw, Poland

来源：

MATHEMATICAL MODELLING OF NATURAL PHENOMENA | 2022年 / 17卷

关键词：

Planar monotone traveling wave front; Reaction-diffusion PDE with delay; Difference equation; Monostable equation; FISHER-KPP EQUATION; ASYMPTOTIC SPEEDS; POPULATION-MODELS; FRONTS; STABILITY; AGE; SPREAD; EXISTENCE; DYNAMICS; SYSTEM;

D O I：

10.1051/mmnp/2022021

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We consider a class of biological models represented by a system composed of reactiondiffusion PDE coupled with difference equations (renewal equations) in n-dimensional space, with nonlocal dispersal terms and implicit time delays. The difference equation generally arises, by means of the method of characteristics, from an age-structured partial differential system. Using upper and lower solutions, we study the existence of monotonic planar traveling wave fronts connecting the extinction state to the uniform positive state. The corresponding minimum wave speed is also obtained. In addition, we investigate the effect of the parameters on this minimum wave speed and we give a detailed analysis of its asymptotic behavior.

引用

页数：31

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