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Turing patterns in the Lengyel-Epstein system for the CIMA reaction. (English) Zbl 1074.35051

The Lengyel-Epstein model for the CIMA reaction has the form

u t =Δu+a-u-4uv/(1+u 2 ),v t =σ(cΔv+b(u-uv/(1+u 2 ))(1)

with the Neumann boundary condition. The authors give a detailed analysis of (1). Among others, they show: (i) System (1) has no nonconstant positive steady solution, if the size of the reactor, or the diffusion rate c/b is not large enough. (ii) System (1) has non-constant positive steady solutions if the diffusion rate c/b is large enough and the parameter a lies in a suitable range.

35K50Systems of parabolic equations, boundary value problems (MSC2000)
35K57Reaction-diffusion equations