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Global bifurcation and structure of Turing patterns in the 1-D Lengyel-Epstein model. (English) Zbl 1072.35091

The authors study the analytical aspects of the Lengyel-Epstein reaction diffusion system that models the formation of the so-called Turing patterns (or more generally non-constant steady states) in the chlorine dioxide reaction. After recalling some relevant results from their earlier paper, the authors provide a detailed discussion of the global bifurcation structure of the set of the non-constant steady states focusing on the one-dimensional case. The discussed bifurcation theory approach relies on results due to Crandall and Rabinowitz, the Rabinowitz global bifurcation theorem and the Leray-Schauder degree theory. Moreover, the limiting behavior of the solution set is analytically described by an appropriate use of the solution to the corresponding shadow system.

MSC:

35K57 Reaction-diffusion equations
34C23 Bifurcation theory for ordinary differential equations
35B32 Bifurcations in context of PDEs
92E20 Classical flows, reactions, etc. in chemistry
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