Spreading speeds of a partially degenerate reaction-diffusion system in a periodic habitat

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Wu, Chufen^1,2  Xiao, Dongmei²  Zhao, Xiao-Qiang³ 

[1] Foshan Univ, Dept Math, Foshan 528000, Peoples R China

[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

[3] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

关键词: Partially degenerate;    Reaction-diffusion system;    Periodic habitat;    Principal eigenvalue;    Spreading speed;   

DOI  :  10.1016/j.jde.2013.07.058

来源: Elsevier

【 摘 要 】

This paper is devoted to the study of the spreading speeds of a partially degenerate reaction-diffusion system with monostable nonlinearity in a periodic habitat. We first obtain sufficient conditions for the existence of principal eigenvalues in the case where solution maps of the associated linear systems lack compactness, and prove a threshold type result on the global dynamics for the periodic initial value problem. Then we establish the existence and computational formulae of spreading speeds for the general initial value problem. It turns out that the spreading speed is linearly determinate. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free