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, Volume 43 (2009) no. 1, p. 151-172

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.

DOI : https://doi.org/10.1051/m2an:2008045
Classification:  35B40,  35B50,  35K57,  80A30,  92E20
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {1},
     year = {2009},
     pages = {151-172},
     doi = {10.1051/m2an:2008045},
     zbl = {1155.35312},
     mrnumber = {2494798},
     language = {en},
     url = {http://www.numdam.org/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, Volume 43 (2009) no. 1, pp. 151-172. doi : 10.1051/m2an:2008045. http://www.numdam.org/item/M2AN_2009__43_1_151_0/

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