Low-Dimensional Manifolds in Reaction−Diffusion Equations. 1. Fundamental Aspects
- 11 March 2006
- journal article
- research article
- Published by American Chemical Society (ACS) in The Journal of Physical Chemistry A
- Vol. 110 (16), 5235-5256
- https://doi.org/10.1021/jp055592s
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.Keywords
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