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.
Mots-clés : entropy methods, Lyapounov functionals, reaction-diffusion equations
@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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {151--172},
publisher = {EDP-Sciences},
volume = {43},
number = {1},
year = {2009},
doi = {10.1051/m2an:2008045},
mrnumber = {2494798},
zbl = {1155.35312},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2008045/}
}
TY - JOUR AU - Bisi, Marzia AU - Desvillettes, Laurent AU - Spiga, Giampiero TI - Exponential convergence to equilibrium via Lyapounov functionals for reaction-diffusion equations arising from non reversible chemical kinetics JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2009 SP - 151 EP - 172 VL - 43 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2008045/ DO - 10.1051/m2an:2008045 LA - en ID - M2AN_2009__43_1_151_0 ER -
%0 Journal Article %A Bisi, Marzia %A Desvillettes, Laurent %A Spiga, Giampiero %T Exponential convergence to equilibrium via Lyapounov functionals for reaction-diffusion equations arising from non reversible chemical kinetics %J ESAIM: Modélisation mathématique et analyse numérique %D 2009 %P 151-172 %V 43 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2008045/ %R 10.1051/m2an:2008045 %G en %F 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: Modélisation mathématique et analyse numérique, Tome 43 (2009) no. 1, pp. 151-172. doi : 10.1051/m2an:2008045. http://www.numdam.org/articles/10.1051/m2an:2008045/
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