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European Mathematical Society Publishing House
2016-09-19 17:05:45
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
24
2008
2
Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds
Laurent
Desvillettes
, CACHAN CEDEX, FRANCE
Klemens
Fellner
Universität Wien, WIEN, AUSTRIA
Reaction-diffusion, entropy method, exponential decay, slowly growing a-priori estimates
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.
Partial differential equations
General
407
431
10.4171/RMI/541
http://www.ems-ph.org/doi/10.4171/RMI/541