Dynamics of a reaction-diffusion system of autocatalytic chemical reaction

Jifa Jiang; Junping Shi

doi:10.3934/dcds.2008.21.245

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2008, Volume 21, Issue 1: 245-258. Doi: 10.3934/dcds.2008.21.245

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Dynamics of a reaction-diffusion system of autocatalytic chemical reaction

Jifa Jiang^1, and
Junping Shi^2,

1.
Department of Mathematics, Tongji University, Shanghai 200092
2.
Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187

Received: December 31, 2006

Revised: April 30, 2007

Published: December 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 35J55; Secondary: 35B40, 80A32.

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