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Exponential convergence to equilibrium via Lyapounov functionals for reaction-diffusion equations arising from non reversible chemical kinetics

Published online by Cambridge University Press:  05 December 2008

Marzia Bisi ,
Laurent Desvillettes  and
Giampiero Spiga
Marzia Bisi
Affiliation:
Dipartimento di Matematica, Università di Parma, Viale G.P. Usberti 53/A, 43100 Parma, Italy. marzia.bisi@unipr.it giampiero.spiga@unipr.it
Laurent Desvillettes
Affiliation:
CMLA, ENS Cachan, IUF & CNRS, PRES UniverSud, 61 avenue du Président Wilson, 94230 Cachan, France. desville@cmla.ens-cachan.fr
Giampiero Spiga
Affiliation:
Dipartimento di Matematica, Università di Parma, Viale G.P. Usberti 53/A, 43100 Parma, Italy. marzia.bisi@unipr.it giampiero.spiga@unipr.it
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Abstract


We show that the entropy method, that has been used successfully in order to prove exponential convergence towards equilibrium with explicit constants in many contexts, among which reaction-diffusion systems coming out of reversible chemistry, can also be used when one considers a reaction-diffusion system corresponding to an irreversible mechanism of dissociation/recombination, for which no natural entropy is available.


Keywords

Entropy methodsLyapounov functionalsreaction-diffusion equations.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 1 , January 2009 , pp. 151 - 172
Copyright
© EDP Sciences, SMAI, 2008

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