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.
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