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Low-dimensional manifolds in reaction-diffusion equations. 1. Fundamental aspects.

Authors
Type
Published Article
Journal
The journal of physical chemistry. A
Publication Date
Volume
110
Issue
16
Pages
5235–5256
Identifiers
PMID: 16623450
Source
Medline
License
Unknown

Abstract

The approach to equilibrium for systems of reaction-diffusion equations on bounded domains is studied geometrically. It is shown that equilibrium is approached via low-dimensional manifolds in the infinite-dimensional function space for these dissipative, parabolic systems. The fundamental aspects of this process are mapped out in some detail for single species cases and for two-species cases where there is an exact solution. It is shown how the manifolds reduce the dimensionality of the system from infinite dimensions to only a few dimensions.

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