On a cross-diffusion system modeling vegetation spots and strips in a semi-arid or arid landscape. (August 2017)

• Record Type: Journal Article
• Authors: Yin, Hong-Ming; Chen, Xinfu; Wang, Lihe
• Is Part Of: Nonlinear analysis. Volume 159(2017)
• Page Start: 482
• Page End: 491
• Publication Date: 2017-08
• Subjects: 35K51 -- 35K57; Vegetation pattern model -- Cross-diffusion system -- Existence and uniqueness; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.02.022
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we study a model which describes the pattern formation of vegetation spots and strips in a semi-arid or arid landscape. The mathematical model consists of a nonlinear cross-diffusion system with evaporation and absorption sources. Global existence and uniqueness in classical sense for the system are established. Some asymptotic behaviors of the solution are derived for a linearized system. It is shown that the solution of the linearized system is asymptotically stable near the steady-state solution. Moreover, we show that the Turing phenomenon occurs for the linearized cross-diffusion system and the cross-diffusion destabilizes the ecosystem.