Survey on Probabilistic Methods for the Study of Kac-like Equations

Federico Bassetti; Ester Gabetta

Bollettino dell'Unione Matematica Italiana (2011)

  • Volume: 4, Issue: 2, page 187-212
  • ISSN: 0392-4041

Abstract

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This mainly explanatory paper shows how direct application of probabilistic methods, pertaining to central limit general theory, can enlighten us about the relaxation to equilibrium of the solutions of one-dimensional Boltzmann type equations. In particular, conditions under which the solutions of these equations converge to suitable scale mixture of stable distributions are reviewed. In addition, some recent results about the rate of convergence to steady states, with respect to various metrics, are summarized. Finally, by resorting to the above mentioned probabilistic methods, some new results related to a linear kinetic model are proven.

How to cite

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Bassetti, Federico, and Gabetta, Ester. "Survey on Probabilistic Methods for the Study of Kac-like Equations." Bollettino dell'Unione Matematica Italiana 4.2 (2011): 187-212. <http://eudml.org/doc/290744>.

@article{Bassetti2011,
abstract = {This mainly explanatory paper shows how direct application of probabilistic methods, pertaining to central limit general theory, can enlighten us about the relaxation to equilibrium of the solutions of one-dimensional Boltzmann type equations. In particular, conditions under which the solutions of these equations converge to suitable scale mixture of stable distributions are reviewed. In addition, some recent results about the rate of convergence to steady states, with respect to various metrics, are summarized. Finally, by resorting to the above mentioned probabilistic methods, some new results related to a linear kinetic model are proven.},
author = {Bassetti, Federico, Gabetta, Ester},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {187-212},
publisher = {Unione Matematica Italiana},
title = {Survey on Probabilistic Methods for the Study of Kac-like Equations},
url = {http://eudml.org/doc/290744},
volume = {4},
year = {2011},
}

TY - JOUR
AU - Bassetti, Federico
AU - Gabetta, Ester
TI - Survey on Probabilistic Methods for the Study of Kac-like Equations
JO - Bollettino dell'Unione Matematica Italiana
DA - 2011/6//
PB - Unione Matematica Italiana
VL - 4
IS - 2
SP - 187
EP - 212
AB - This mainly explanatory paper shows how direct application of probabilistic methods, pertaining to central limit general theory, can enlighten us about the relaxation to equilibrium of the solutions of one-dimensional Boltzmann type equations. In particular, conditions under which the solutions of these equations converge to suitable scale mixture of stable distributions are reviewed. In addition, some recent results about the rate of convergence to steady states, with respect to various metrics, are summarized. Finally, by resorting to the above mentioned probabilistic methods, some new results related to a linear kinetic model are proven.
LA - eng
UR - http://eudml.org/doc/290744
ER -

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