Exponential Convergence to Equilibrium for Nonlinear Reaction-Diffusion Systems Arising in Reversible Chemistry

Abstract : We consider a prototypical nonlinear reaction-diffusion system arising in reversible chemistry. Based on recent existence results of global weak and classical solutions derived from entropy-decay related a-priori estimates and duality methods, we prove exponential convergence of these solutions towards equilibrium with explicit rates in all space dimensions.The key step of the proof establishes an entropy entropy-dissipation estimate, which relies only on natural a-priori estimates provided by mass-conservation laws and the decay of an entropy functional.
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Laurent Desvillettes, Klemens Fellner. Exponential Convergence to Equilibrium for Nonlinear Reaction-Diffusion Systems Arising in Reversible Chemistry. 26th Conference on System Modeling and Optimization (CSMO), Sep 2013, Klagenfurt, Austria. pp.96-104, ⟨10.1007/978-3-662-45504-3_9⟩. ⟨hal-01286402⟩

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