Entropic approximation in kinetic theory
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 3, p. 541-561

Approximation theory in the context of probability density function turns out to go beyond the classical idea of orthogonal projection. Special tools have to be designed so as to respect the nonnegativity of the approximate function. We develop here and justify from the theoretical point of view an approximation procedure introduced by Levermore [Levermore, J. Stat. Phys. 83 (1996) 1021-1065] and based on an entropy minimization principle under moment constraints. We prove in particular a global existence theorem for such an approximation and derive as a by-product a necessary and sufficient condition for the so-called problem of moment realizability. Applications of the above result are given in kinetic theory: first in the context of Levermore's approach and second to design generalized BGK models for Maxwellian molecules.

DOI : https://doi.org/10.1051/m2an:2004025
Classification:  54C70,  46N10,  82B40,  37L65
Keywords: kinetic entropy, convex analysis, nonlinear approximation, moments systems, maxwellian molecules
@article{M2AN_2004__38_3_541_0,
author = {Schneider, Jacques},
title = {Entropic approximation in kinetic theory},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {38},
number = {3},
year = {2004},
pages = {541-561},
doi = {10.1051/m2an:2004025},
zbl = {1084.82010},
mrnumber = {2075759},
language = {en},
url = {http://www.numdam.org/item/M2AN_2004__38_3_541_0}
}

Schneider, Jacques. Entropic approximation in kinetic theory. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 3, pp. 541-561. doi : 10.1051/m2an:2004025. http://www.numdam.org/item/M2AN_2004__38_3_541_0/

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