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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.
@article{M2AN_2004__38_3_541_0,
author = {Schneider, Jacques},
title = {Entropic approximation in kinetic theory},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {541--561},
publisher = {EDP-Sciences},
volume = {38},
number = {3},
year = {2004},
doi = {10.1051/m2an:2004025},
mrnumber = {2075759},
zbl = {1084.82010},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004025/}
}
TY - JOUR AU - Schneider, Jacques TI - Entropic approximation in kinetic theory JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2004 SP - 541 EP - 561 VL - 38 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004025/ DO - 10.1051/m2an:2004025 LA - en ID - M2AN_2004__38_3_541_0 ER -
%0 Journal Article %A Schneider, Jacques %T Entropic approximation in kinetic theory %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2004 %P 541-561 %V 38 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004025/ %R 10.1051/m2an:2004025 %G en %F M2AN_2004__38_3_541_0
Schneider, Jacques. Entropic approximation in kinetic theory. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 3, pp. 541-561. doi: 10.1051/m2an:2004025
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