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Transactions of the American Mathematical Society

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


Authors: Wei-Ming Ni and Moxun Tang
Journal: Trans. Amer. Math. Soc. 357 (2005), 3953-3969
MSC (2000): Primary 35K50, 35K57, 92D25
DOI: https://doi.org/10.1090/S0002-9947-05-04010-9
Published electronically: May 20, 2005
MathSciNet review: 2159695
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Abstract: The first experimental evidence of the Turing pattern was observed 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 properties 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. A priori estimates are fundamental to our approach for this nonexistence result. The degree theory was combined with the a priori estimates to derive existence of nonconstant steady states.


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Additional Information

Wei-Ming Ni
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: ni@math.umn.edu

Moxun Tang
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: mtang@math.msu.edu

DOI: https://doi.org/10.1090/S0002-9947-05-04010-9
Received by editor(s): June 16, 2003
Published electronically: May 20, 2005
Article copyright: © Copyright 2005 American Mathematical Society

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