# Entropic approximation in kinetic theory

- Volume: 38, Issue: 3, page 541-561
- ISSN: 0764-583X

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topSchneider, Jacques. "Entropic approximation in kinetic theory." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 38.3 (2004): 541-561. <http://eudml.org/doc/245932>.

@article{Schneider2004,

abstract = {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.},

author = {Schneider, Jacques},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {kinetic entropy; convex analysis; nonlinear approximation; moments systems; maxwellian molecules; Entropic approximation; moment closure; kinetic theory},

language = {eng},

number = {3},

pages = {541-561},

publisher = {EDP-Sciences},

title = {Entropic approximation in kinetic theory},

url = {http://eudml.org/doc/245932},

volume = {38},

year = {2004},

}

TY - JOUR

AU - Schneider, Jacques

TI - Entropic approximation in kinetic theory

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2004

PB - EDP-Sciences

VL - 38

IS - 3

SP - 541

EP - 561

AB - 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.

LA - eng

KW - kinetic entropy; convex analysis; nonlinear approximation; moments systems; maxwellian molecules; Entropic approximation; moment closure; kinetic theory

UR - http://eudml.org/doc/245932

ER -

## References

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