Hypocoercive Diffusion Operators

Cédric Villani

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 2, page 257-275
  • ISSN: 0392-4033

Abstract

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In many problems coming from mathematical physics, the association of a degenerate diffusion operator with a conservative operator may lead to dissipation in all variables and convergence to equilibrium. One can draw an analogy with the well-studied phenomenon of hypoellipticity in regularity theory, and actually both phenomena have been studied together. Now a distinctive theory of ``hypocoercivity'' is starting to emerge, with already some striking results, and several challenging open problems. This text (an abbreviated version of the one which I prepared for the International Congress of Mathematicians) will review some of them.

How to cite

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Villani, Cédric. "Hypocoercive Diffusion Operators." Bollettino dell'Unione Matematica Italiana 10-B.2 (2007): 257-275. <http://eudml.org/doc/290402>.

@article{Villani2007,
abstract = {In many problems coming from mathematical physics, the association of a degenerate diffusion operator with a conservative operator may lead to dissipation in all variables and convergence to equilibrium. One can draw an analogy with the well-studied phenomenon of hypoellipticity in regularity theory, and actually both phenomena have been studied together. Now a distinctive theory of ``hypocoercivity'' is starting to emerge, with already some striking results, and several challenging open problems. This text (an abbreviated version of the one which I prepared for the International Congress of Mathematicians) will review some of them.},
author = {Villani, Cédric},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {257-275},
publisher = {Unione Matematica Italiana},
title = {Hypocoercive Diffusion Operators},
url = {http://eudml.org/doc/290402},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Villani, Cédric
TI - Hypocoercive Diffusion Operators
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/6//
PB - Unione Matematica Italiana
VL - 10-B
IS - 2
SP - 257
EP - 275
AB - In many problems coming from mathematical physics, the association of a degenerate diffusion operator with a conservative operator may lead to dissipation in all variables and convergence to equilibrium. One can draw an analogy with the well-studied phenomenon of hypoellipticity in regularity theory, and actually both phenomena have been studied together. Now a distinctive theory of ``hypocoercivity'' is starting to emerge, with already some striking results, and several challenging open problems. This text (an abbreviated version of the one which I prepared for the International Congress of Mathematicians) will review some of them.
LA - eng
UR - http://eudml.org/doc/290402
ER -

References

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