, Volume 51, Issue 2, pp 637-659

Stationary patterns in a two-cell coupled isothermal chemical system with arbitrary powers of autocatalysis

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Abstract

Stationary patterns of a two-cell coupled isothermal chemical system with arbitrary powers of autocatalysis are considered. Firstly, we obtain the stability of the unique positive constant equilibrium solution for the system. Then, based on a priori estimates, non-existence and existence of nontrivial steady state solutions are shown by using implicit function theorem and topological degree theory, respectively. The effects of autocatalysis order and diffusion coefficients to the pattern formation are discussed.

Supported by the NNSF of China (Nos. 10971231, 11071238 and 11271379).