Entropy methods for reaction-diffusion systems

Laurent Desvillettes; Klemens Fellner

doi:10.3934/proc.2007.2007.304

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2007, Volume 2007: 304-312. Doi: 10.3934/proc.2007.2007.304 open access

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Entropy methods for reaction-diffusion systems

Laurent Desvillettes^1, and
Klemens Fellner^2,

1.
ENS Cachan, CMLA, IUF & CNRS, PRES UniverSud, 61, Av. du Pdt Wilson, 94235 Cachan Cedex
2.
Faculty of Mathematics, University of Vienna, Nordbergstr. 15, 1090 Wien

Received: June 30, 2006

Revised: March 31, 2007

Published: August 2007

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Abstract

In the continuation of [6], we study reversible reaction-diffusion systems via entropy methods (based on the free energy functional). We show for a particular model problem with two reacting species in which one of the diffusion constants vanishes that the solutions decay exponentially with explicit rate and constant towards the unique constant equilibrium state.

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Mathematics Subject Classification: 35B40, 35K57.

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