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.
@article{M2AN_2009__43_1_151_0,
author = {Bisi, Marzia and Desvillettes, Laurent and Spiga, Giampiero},
title = {Exponential convergence to equilibrium via Lyapounov functionals for reaction-diffusion equations arising from non reversible chemical kinetics},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {43},
year = {2009},
pages = {151-172},
doi = {10.1051/m2an:2008045},
mrnumber = {2494798},
zbl = {1155.35312},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2009__43_1_151_0}
}
Bisi, Marzia; Desvillettes, Laurent; Spiga, Giampiero. Exponential convergence to equilibrium via Lyapounov functionals for reaction-diffusion equations arising from non reversible chemical kinetics. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 43 (2009) pp. 151-172. doi : 10.1051/m2an:2008045. http://gdmltest.u-ga.fr/item/M2AN_2009__43_1_151_0/
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