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Entropy methods for reaction-diffusion systems

Pages: 304 - 312, Issue Special, September 2007

 Abstract        Full Text (224.1K)              

Laurent Desvillettes - ENS Cachan, CMLA, IUF & CNRS, PRES UniverSud, 61, Av. du Pdt Wilson, 94235 Cachan Cedex, France (email)
Klemens Fellner - Faculty of Mathematics, University of Vienna, Nordbergstr. 15, 1090 Wien, Austria (email)

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.

Keywords:  Reaction-Diffusion, Entropy Method, Exponential Decay, Degenerate Diffusion.
Mathematics Subject Classification:  35B40, 35K57.

Received: July 2006;      Revised: April 2007;      Published: September 2007.