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


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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@article{Davis2006LowdimensionalMI, title={Low-dimensional manifolds in reaction-diffusion equations. 1. Fundamental aspects.}, author={Michael J Davis}, journal={The journal of physical chemistry. A}, year={2006}, volume={110 16}, pages={5235-56} }