Forced waves of the Fisher-KPP equation in a shifting environment

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Berestycki, Henri¹  Fang, Jian^2,3 

[1] PSL Res Univ, CNRS, Ctr Anal & Math Sociales, Ecole Hautes Etud Sci Sociales, Paris, France

[2] Harbin Inst Technol, Inst Adv Study Math, Harbin, Heilongjiang, Peoples R China

[3] Harbin Inst Technol, Dept Math, Harbin, Heilongjiang, Peoples R China

关键词: Shifting environment;    Fisher-KPP equation;    Traveling waves;    Long time behavior;   

DOI  :  10.1016/j.jde.2017.10.016

来源: Elsevier

【 摘 要 】

This paper concerns the equation u(t) = u(xx) + f(x - ct, u), x is an element of R, (0,1) where c >= 0 is a forcing speed and f : (s, u) is an element of R x R+ -> R is asymptotically of KPP type as s -> -infinity. We are interested in the questions of whether such a forced moving KPP nonlinearity from behind can give rise to traveling waves with the same speed and how they attract solutions of initial value problems when they exist. Under a sublinearity condition on f(s, u), we obtain the complete existence and multiplicity of forced traveling waves as well as their attractivity except for some critical cases, fn these cases, we provide examples to show that there is no definite answer unless one imposes further conditions depending on the heterogeneity of f in s is an element of R. (c) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free