Comptes Rendus
no. 11
From microscopic to macroscopic descriptions of complex systems
[De la description microscopique à la description macroscopique des systèmes complexes]

Présenté par : Evariste Sanchez-Palencia

Mirosław Lachowicz1
1 Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland
Comptes Rendus. Mécanique, Volume 331 (2003) no. 11, pp. 733-738.

Nous considérons ici des systèmes complexes descrits au niveau macroscopique par des EDOs bilinéaires ou par des équations de réaction–diffusion bilinéaires. La description microscopique correspondante est définie. Les relations mathématiques entre les deux descriptions sont formulées. Les solutions des équations macroscopiques bilinéaires sont approximées par des semigroupes stochastiques (linéaires) et l'ordre d'approximation est donné.

Complex systems that can be described at the macroscopic level in terms of bilinear ODEs or bilinear reaction–diffusion equations are considered. The corresponding microscopic description at the level of stochastically interacting entities is defined. The mathematical relationships between these two descriptions are formulated. The solutions of bilinear macroscopic equations are approximated by stochastic (linear) semigroups and the order of approximation is given.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2003.09.003
Keywords: Continuum mechanics, Complex systems, ODE, Reaction–diffusion equations, Stochastic semigroups
Mot clés : Millieux continus, Systèmes complexes, EDO, Équations de réaction-diffusion, Semigroupes stochastiques
Mirosław Lachowicz 1

1 Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland 
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Mirosław Lachowicz. From microscopic to macroscopic descriptions of complex systems. Comptes Rendus. Mécanique, Volume 331 (2003) no. 11, pp. 733-738. doi : 10.1016/j.crme.2003.09.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2003.09.003/

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[12] M. Lachowicz Describing competitive systems at the level of interacting individuals, Proceedings of the Eight National Conference on Applications of Mathematics in Biology and Medicine, Łajs, 25–28 September, 2002, pp. 95-100

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