Annales Mathématiques
Blaise Pascal
no. 1
Solution of a class of reaction-diffusion systems via logarithmic Sobolev inequality
Pierre Fougères1 ; Ivan Gentil2 ; Boguslaw Zegarliński3
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.

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 :
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.

Pierre Fougères 1 ; Ivan Gentil 2 ; Boguslaw Zegarliński 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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Pierre Fougères; Ivan Gentil; Boguslaw Zegarliński. 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. https://ambp.centre-mersenne.org/articles/10.5802/ambp.363/

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