Hypocoercive Diffusion Operators

IF 0.7 Q2 MATHEMATICS

BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA Pub Date : 2006-01-01 DOI:10.4171/022-3/25

C. Villani

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.

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准强制扩散算子

在许多数学物理问题中，简并扩散算子与保守算子的关联可能导致所有变量的耗散和收敛到平衡态。人们可以将其与正则性理论中研究得很充分的亚椭圆现象进行类比，实际上这两种现象是一起研究的。现在，一种独特的“低强制”理论开始出现，已经有了一些惊人的结果，以及一些具有挑战性的开放问题。数学学科分类(2000)。主要35 3;二级35K70, 76P05。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA MATHEMATICS-

CiteScore

1.60

自引率

0.00%

发文量

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.