Solution of a class of reaction-diffusion systems via logarithmic Sobolev inequality

Fougères, Pierre; Gentil, Ivan; Zegarliński, Boguslaw

doi:10.5802/ambp.363

Fougères, Pierre ¹ ; Gentil, Ivan ² ; Zegarliński, Boguslaw ³

¹ Institut de Mathématiques de Toulouse, CNRS UMR 5219 Université de Toulouse Route de Narbonne 31062 Toulouse, France
² Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France
³ Imperial College, London South Kensington Campus London SW7 2AZ, United Kingdom

Annales mathématiques Blaise Pascal, Tome 24 (2017) no. 1, pp. 1-53.

Résumé
Abstract

Nous étudions l’existence globale, l’unicité et la positivité de solutions faibles pour une classe de systèmes de réaction-diffusion provenant d’équations chimiques. Le théorème principal repose uniquement sur une inégalité de Sobolev logarithmique et sur l’intégrabilité exponentielle des conditions initiales. En particulier nous développons une stratégie indépendante de la dimension dans un domaine non borné.

We study global existence, uniqueness and positivity of weak solutions of a class of reaction-diffusion systems coming from chemical reactions. The principal result is based only on a logarithmic Sobolev inequality and the exponential integrability of the initial data. In particular we develop a strategy independent of dimensions in an unbounded domain.

Publié le : 2017-08-25

DOI : 10.5802/ambp.363

Classification : 28B10, 35K57, 35R15
Keywords: Reaction-diffusion systems, Markov semigroups, logarithmic Sobolev inequality, infinite dimensions.
Mots clés : Reaction-diffusion systems, Markov semigroups, logarithmic Sobolev inequality, infinite dimensions.

Affiliations des auteurs :

Fougères, Pierre ¹ ; Gentil, Ivan ² ; Zegarliński, Boguslaw ³

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Fougères, Pierre; Gentil, Ivan; Zegarliński, Boguslaw. Solution of a class of reaction-diffusion systems via logarithmic Sobolev inequality. Annales mathématiques Blaise Pascal, Tome 24 (2017) no. 1, pp. 1-53. doi : 10.5802/ambp.363. http://www.numdam.org/articles/10.5802/ambp.363/

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