Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

Steady states of a Sel'kov-Schnakenberg reaction-diffusion system

Pages: 1009 - 1023, Volume 10, Issue 5, October 2017      doi:10.3934/dcdss.2017053

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Bo Li - School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China (email)
Xiaoyan Zhang - School of Mathematics, Shandong University, Jinan, Shandong 250100, China (email)

Abstract: In this paper, we are concerned with a reaction-diffusion model, known as the Sel'kov-Schnakenberg system, and study the associated steady state problem. We obtain existence and nonexistence results of nonconstant steady states, which in turn imply the criteria for the formation of spatial pattern (especially, Turing pattern). Our results reveal the different roles of the diffusion rates of the two reactants in generating spatial pattern.

Keywords:  Sel'kov-Schnakenberg reaction-diffusion system, steady state, spatial pattern, Turing pattern, existence.
Mathematics Subject Classification:  Primary: 35J57, 35J61, 35K57; Secondary: 35B36, 92C40.

Received: September 2016;      Revised: February 2017;      Available Online: June 2017.