Transition waves for two species competition system in time heterogeneous media. (December 2018)

• Record Type: Journal Article
• Authors: Bao, Xiongxiong
• Is Part Of: Nonlinear analysis. Volume 44(2018)
• Page Start: 128
• Page End: 148
• Publication Date: 2018-12
• Subjects: Two species competition system -- Transition wave -- Time heterogeneous media -- Spreading speed intervals -- Existence; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.04.009
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is concerned with the spreading speeds and transition waves of the following two species competition system in time heterogeneous media, u t = Δ u + u ( a 1 ( t ) − b 1 ( t ) u − c 1 ( t ) v ), v t = Δ v + v ( a 2 ( t ) − b 2 ( t ) u − c 2 ( t ) v ), x ∈ R N, t ∈ R, where a i ( ⋅ ), b i ( ⋅ ), c i ( ⋅ ) ( i = 1, 2 ) depend in a general way in t ∈ R . The notion of transition waves for such a system is first introduced in this paper. We first establish the lower bounds of spreading speed intervals and generalized spreading speed intervals. It then shows that, under certain conditions, there exists a pair of general transition waves ( u ( t, x ), v ( t, x ) ) connecting two semitrivial solutions of this system for a given class of speed c ( t ) with c ̲ > c ∗ and for any c ̲ < c ∗, there is no such transition waves.