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

Handle URI:
http://hdl.handle.net/10754/598199
Title:
Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds
Authors:
Desvillettes, Laurent; Fellner, Klemens
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.
Citation:
Desvillettes L, Fellner K (2008) Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds. Rev Mat Iberoamericana: 407–431. Available: http://dx.doi.org/10.4171/rmi/541.
Publisher:
European Mathematical Publishing House
Journal:
Revista Matemática Iberoamericana
Issue Date:
2008
DOI:
10.4171/rmi/541
Type:
Article
ISSN:
0213-2230
Sponsors:
This work has been supported by the European IHP network “HYKE-HYperbolic andKinetic Equations: Asymptotics, Numerics, Analysis”, Contract Number: HPRN-CT-2002-00282. K.F. has also been supported by the Austrian Science Fund FWF projectP16174-N05, by theWittgenstein Award 2000 of Peter A. Markowich, and by the KAUSTinvestigator award 2008 of Peter A. Markowich.
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Full metadata record

DC FieldValue Language
dc.contributor.authorDesvillettes, Laurenten
dc.contributor.authorFellner, Klemensen
dc.date.accessioned2016-02-25T13:14:34Zen
dc.date.available2016-02-25T13:14:34Zen
dc.date.issued2008en
dc.identifier.citationDesvillettes L, Fellner K (2008) Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds. Rev Mat Iberoamericana: 407–431. Available: http://dx.doi.org/10.4171/rmi/541.en
dc.identifier.issn0213-2230en
dc.identifier.doi10.4171/rmi/541en
dc.identifier.urihttp://hdl.handle.net/10754/598199en
dc.description.abstractIn 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.en
dc.description.sponsorshipThis work has been supported by the European IHP network “HYKE-HYperbolic andKinetic Equations: Asymptotics, Numerics, Analysis”, Contract Number: HPRN-CT-2002-00282. K.F. has also been supported by the Austrian Science Fund FWF projectP16174-N05, by theWittgenstein Award 2000 of Peter A. Markowich, and by the KAUSTinvestigator award 2008 of Peter A. Markowich.en
dc.publisherEuropean Mathematical Publishing Houseen
dc.titleEntropy methods for reaction-diffusion equations: slowly growing a-priori boundsen
dc.typeArticleen
dc.identifier.journalRevista Matemática Iberoamericanaen
dc.contributor.institutionCMLA-ENS, 61, Av du Président Wilson, 94235, CACHAN CEDEX, FRANCEen
dc.contributor.institutionInstitut für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090, WIEN, AUSTRIAen
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