Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds

Laurent Desvillettes, Klemens Fellner

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Abstract

In the continuation of [Desvillettes, L., Fellner, K.: Exponential Decay toward Equilibrium via Entropy Methods for Reaction-Diffusion Equations. J. Math. Anal. Appl. 319 (2006), no. 1, 157-176], we study reversible reaction-diffusion equations via entropy methods (based on the free energy functional) for a 1D system of four species. We improve the existing theory by getting 1) almost exponential convergence in L1 to the steady state via a precise entropy-entropy dissipation estimate, 2) an explicit global L∞ bound via interpolation of a polynomially growing H1 bound with the almost exponential L1 convergence, and 3), finally, explicit exponential convergence to the steady state in all Sobolev norms.
Original languageEnglish (US)
Pages (from-to)407-431
Number of pages25
JournalRevista Matemática Iberoamericana
Volume24
Issue number2
DOIs
StatePublished - 2008
Externally publishedYes

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