Solution of a class of reaction-diffusion systems via logarithmic Sobolev inequality
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 : 2017-08-24
DOI : https://doi.org/10.5802/ambp.363
Classification : 28B10,  35K57,  35R15
Mots clés: Reaction-diffusion systems, Markov semigroups, logarithmic Sobolev inequality, infinite dimensions.
@article{AMBP_2017__24_1_1_0,
     author = {Pierre Foug\`eres and Ivan Gentil and Boguslaw Zegarli\'nski},
     title = {Solution of a class of reaction-diffusion systems via logarithmic Sobolev inequality},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {1--53},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {24},
     number = {1},
     year = {2017},
     doi = {10.5802/ambp.363},
     language = {en},
     url = {ambp.centre-mersenne.org/item/AMBP_2017__24_1_1_0/}
}
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/item/AMBP_2017__24_1_1_0/

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