{"title":"Hypocoercive Diffusion Operators","authors":"C. Villani","doi":"10.4171/022-3/25","DOIUrl":null,"url":null,"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. Mathematics Subject Classification (2000). Primary 35B40; Secondary 35K70, 76P05.","PeriodicalId":54191,"journal":{"name":"BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA","volume":"8 1","pages":"257-276"},"PeriodicalIF":0.7000,"publicationDate":"2006-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"68","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/022-3/25","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 68
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. Mathematics Subject Classification (2000). Primary 35B40; Secondary 35K70, 76P05.
期刊介绍：
The Bollettino dell''Unione Matematica Italiana (BUMI) is the scientific journal of Unione Matematica Italiana: it publishes original research and high quality survey articles in all fields of Mathematics. There is no upper limit to the number of pages per article. The Unione Matematica Italiana was founded by Salvatore Pincherle in 1922, and has published BUMI since then. Articles published in BUMI will be freely available to the general public on SpringerLink 5 years after publication.
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