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The first experimental evidence of the Turing pattern was ob- served by De Kepper and her associates (1990) on the CIMA reaction in an open unstirred gel reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction- diffusion equations. In this paper we report some fundamental analytic prop- erties of the Lengyel-Epstein system. Our result also indicates that if either of the initial concentrations of the reactants, the size of the reactor, or the effective diffusion rate, are not large enough, then the system does not admit nonconstant steady states. Ap rioriestimates are fundamental to our ap- proach for this nonexistence result. The degree theory was combined with the ap rioriestimates to derive existence of nonconstant steady states.

Turing patterns in the Lengyel-Epstein system for the CIMA reaction