Asymptotic behavior of traveling fronts and entire solutions for a periodic bistable competition-diffusion system

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:265

Article

Du, Li-Jun¹  Li, Wan-Tong¹  Wang, Jia-Bing² 

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China

[2] China Univ Geosci Wuhan, Sch Math & Phys, Wuhan 430074, Hubei, Peoples R China

关键词: Periodic traveling front;    Asymptotic behavior;    Comparison principle;    Entire solution;    New spreading ways;   

DOI  :  10.1016/j.jde.2018.07.024

来源: Elsevier

【 摘 要 】

This paper is concerned with a time periodic competition-diffusion system {u(t) = u(xx) + u(r(1)(t) - a(1)(t)u - b(1)(t)v), t > 0, x is an element of R, v(t) = dv(xx) + v(r(2)(t) - a(2)(t)u - b(2)(t)v), t > 0, x is an element of R, where u(t, x) and v(t, x) denote the densities of two competing species, d > 0 is some constant, r(i) (t), a(i) (t) and b(i) (t) are T-periodic continuous functions. Under suitable conditions, it has been confirmed by Bao and Wang (2013) [2] that this system admits periodic traveling fronts connecting two stable semi-trivial T-periodic solutions (p(t), 0) and (0, q(t)) associated to the corresponding kinetic system. In the present work, we first investigate the asymptotic behavior of periodic bistable traveling fronts with non-zero speeds at infinity by a dynamical approach combined with the two-sided Laplace transform method. With these asymptotic properties, we then obtain some key estimates. As a result, by applying the super- and subsolutions techniques as well as the comparison principle, we establish the existence and various qualitative properties of the so-called entire solutions defined for all time and the whole space, which provides some new spreading ways other than periodic traveling waves for two strongly competing species interacting in a heterogeneous environment. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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