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July, 2008 Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds
Laurent Desvillettes , Klemens Fellner
Rev. Mat. Iberoamericana 24(2): 407-431 (July, 2008).


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 $L^1$ to the steady state via a precise entropy-entropy dissipation estimate, 2) an explicit global $L^{\infty}$ bound via interpolation of a polynomially growing $H^1$ bound with the almost exponential $L^1$ convergence, and 3), finally, explicit exponential convergence to the steady state in all Sobolev norms.


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Laurent Desvillettes . Klemens Fellner . "Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds." Rev. Mat. Iberoamericana 24 (2) 407 - 431, July, 2008.


Published: July, 2008
First available in Project Euclid: 11 August 2008

zbMATH: 1171.35330
MathSciNet: MR2459198

Primary: 35B40 , 35K57

Keywords: entropy method , Exponential decay , Reaction-diffusion , slowly growing a-priori estimates

Rights: Copyright © 2008 Departamento de Matemáticas, Universidad Autónoma de Madrid


Vol.24 • No. 2 • July, 2008
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