# Trend to equilibrium and spectral localization properties for the linear Boltzmann equation

Daniel Han-Kwan^{[1]}; Matthieu Léautaud^{[2]}

- [1] CNRS and École Polytechnique Centre de Mathématiques Laurent Schwartz UMR7640 F91128 Palaiseau cedex
- [2] Université Paris Diderot Institut de Mathématiques de Jussieu Paris Rive Gauche Bâtiment Sophie Germain 75205 Paris Cedex 13 France

Séminaire Laurent Schwartz — EDP et applications (2013-2014)

- page 1-15
- ISSN: 2266-0607

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topHan-Kwan, Daniel, and Léautaud, Matthieu. "Trend to equilibrium and spectral localization properties for the linear Boltzmann equation." Séminaire Laurent Schwartz — EDP et applications (2013-2014): 1-15. <http://eudml.org/doc/275675>.

@article{Han2013-2014,

abstract = {The aim of this note is to present the results from [11, 12], which deal with the linear Boltzmann equation, set in a bounded domain and in the presence of an external force. A specificity of these works is that the collision operator is allowed to be degenerate in the following two senses: (1) the associated collision kernel may vanish in a large subset of the phase space; (2) we do not assume that it is bounded below by a Maxwellian at infinity in velocity.We study:the large time behavior of solutions of the linear Boltzmann equation, by giving criteria (inspired from control theory) which ensure converge towards an equilibrium and when possible, convergence at an exponential rate [11] ;some properties of localization for the spectrum of the associated operator [12].},

affiliation = {CNRS and École Polytechnique Centre de Mathématiques Laurent Schwartz UMR7640 F91128 Palaiseau cedex; Université Paris Diderot Institut de Mathématiques de Jussieu Paris Rive Gauche Bâtiment Sophie Germain 75205 Paris Cedex 13 France},

author = {Han-Kwan, Daniel, Léautaud, Matthieu},

journal = {Séminaire Laurent Schwartz — EDP et applications},

language = {eng},

pages = {1-15},

publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},

title = {Trend to equilibrium and spectral localization properties for the linear Boltzmann equation},

url = {http://eudml.org/doc/275675},

year = {2013-2014},

}

TY - JOUR

AU - Han-Kwan, Daniel

AU - Léautaud, Matthieu

TI - Trend to equilibrium and spectral localization properties for the linear Boltzmann equation

JO - Séminaire Laurent Schwartz — EDP et applications

PY - 2013-2014

PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique

SP - 1

EP - 15

AB - The aim of this note is to present the results from [11, 12], which deal with the linear Boltzmann equation, set in a bounded domain and in the presence of an external force. A specificity of these works is that the collision operator is allowed to be degenerate in the following two senses: (1) the associated collision kernel may vanish in a large subset of the phase space; (2) we do not assume that it is bounded below by a Maxwellian at infinity in velocity.We study:the large time behavior of solutions of the linear Boltzmann equation, by giving criteria (inspired from control theory) which ensure converge towards an equilibrium and when possible, convergence at an exponential rate [11] ;some properties of localization for the spectrum of the associated operator [12].

LA - eng

UR - http://eudml.org/doc/275675

ER -

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