[Un principe général d'entropie pour les modèles de population structurés et les équations de scattering]
Nous considérons divers modèles de populations structurées (en âge, en taille ou en maturité) et aussi l'équation de scattering. Ces modèles ne sont pas conservatifs, néammoins nous montrons qu'ils vérifient tous une structure d'entropie relative commune qui utilise les premiers éléments propres du problème et qui, dans le cas du scattering, généralise le « principe d'équilibre en détail » habituel. Trois types de conséquences découlent de cette structure entropique : des estimations a priori, la convergence en temps grand vers un état stationnaire et parfois des taux exponentiels de convergence.
We consider several structured population models (age structured, size structured, maturity structured) and the general scattering equation. These models are not conservation laws, nevertheless, we show that they admit a common relative entropy structure which uses the first eigenelements of the problem. In case of scattering, it is more general than the usual ‘detailed balance principle’. Three types of consequences are deduced from this entropy structure: a priori bounds, large time convergence to the steady state and in some cases, exponential rates of convergence.
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@article{CRMATH_2004__338_9_697_0,
author = {Philippe Michel and St\'ephane Mischler and Beno{\i}̂t Perthame},
title = {General entropy equations for structured population models and scattering},
journal = {Comptes Rendus. Math\'ematique},
pages = {697--702},
publisher = {Elsevier},
volume = {338},
number = {9},
year = {2004},
doi = {10.1016/j.crma.2004.03.006},
language = {en},
}
TY - JOUR AU - Philippe Michel AU - Stéphane Mischler AU - Benoı̂t Perthame TI - General entropy equations for structured population models and scattering JO - Comptes Rendus. Mathématique PY - 2004 SP - 697 EP - 702 VL - 338 IS - 9 PB - Elsevier DO - 10.1016/j.crma.2004.03.006 LA - en ID - CRMATH_2004__338_9_697_0 ER -
Philippe Michel; Stéphane Mischler; Benoı̂t Perthame. General entropy equations for structured population models and scattering. Comptes Rendus. Mathématique, Volume 338 (2004) no. 9, pp. 697-702. doi : 10.1016/j.crma.2004.03.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.03.006/
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