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Qualitative analysis on positive steady-states for an autocatalytic reaction model in thermodynamics. (English) Zbl 1371.35084
Summary: In this paper, a reaction-diffusion system known as an autocatalytic reaction model is considered. The model is characterized by a system of two differential equations which describe a type of complex biochemical reaction. Firstly, some basic characterizations of steady-state solutions of the model are presented. And then, the stability of positive constant steady-state solution and the non-existence, existence of non-constant positive steady-state solutions are discussed. Meanwhile, the bifurcation solution which emanates from positive constant steady-state is investigated, and the global analysis to the system is given in one dimensional case. Finally, a few numerical examples are provided to illustrate some corresponding analytic results.

##### MSC:
 35J57 Boundary value problems for second-order elliptic systems 35K57 Reaction-diffusion equations 92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
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