# Hypocoercive Diffusion Operators

Bollettino dell'Unione Matematica Italiana (2007)

- Volume: 10-B, Issue: 2, page 257-275
- ISSN: 0392-4041

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topVillani, 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 -

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