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Dynamics of a reaction-diffusion system of autocatalytic chemical reaction
The precise dynamics of a reaction-diffusion model of autocatalytic
chemical reaction is described. It is shown that exactly either one, two,
or three steady states exists, and the solution of dynamical problem always approaches
to one of steady states in the long run. Moreover it is shown that a global codimension one
manifold separates the basins of attraction of the two stable steady states.
Analytic ingredients include exact multiplicity of semilinear elliptic equation,
the theory of monotone dynamical systems and the
theory of asymptotically autonomous dynamical systems.