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

The Journal of Physical Chemistry. a
Michael J Davis

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.

References

Feb 19, 2002·Chemical Reviews·Miles S. Okino, Michael L. Mavrovouniotis
Jun 5, 2003·Chaos·Marc R. Roussel, Simon J. Fraser

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Citations

Jul 5, 2013·Journal of the Royal Society, Interface·Karl Friston
Jan 10, 2012·Computational and Mathematical Methods in Medicine·Karl Friston, Ping Ao
Dec 4, 2012·Entropy·Friston Karl
Dec 25, 2010·NeuroImage·Karl J FristonKlaas E Stephan
Jan 23, 2017·The Journal of Chemical Physics·Aurel JurjiuFlaviu Turcu
Mar 1, 2018·Scientific Reports·Aurel JurjiuMircea Galiceanu
Feb 6, 2018·Computational Psychiatry·Karl J FristonJoshua A Gordon
Apr 10, 2019·Polymers·Aurel Jurjiu, Mircea Galiceanu
Aug 10, 2007·The Journal of Physical Chemistry. a·Zhuyin Ren, Stephen B Pope
Aug 8, 2008·The Journal of Physical Chemistry. a·Michael J Davis, Alison S Tomlin
Aug 8, 2008·The Journal of Physical Chemistry. a·Michael J Davis, Alison S Tomlin

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