Diffusion and kinetic transport with very weak confinement

Thumbnail
View/Open
Date
2020
Dewey
Analyse
Sujet
Nash’s inequality; Caffarelli-Kohn-Nirenberg inequalities; decay rates; semigroup; weak Poincar inequality; unbounded invariant measure; rate of convergence; Fokker-Planck operator; kinetic equations; scattering operator; transport operator; hypocoercivity
Journal issue
Kinetic & Related Models
Volume
13
Number
2
Publication date
2020
Article pages
345-371
Publisher
AIMS - American Institute of Mathematical Sciences
DOI
http://dx.doi.org/10.3934/krm.2020012
URI
https://basepub.dauphine.fr/handle/123456789/20370
Collections
Metadata
Show full item record
Author
Bouin, Emeric
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Dolbeault, Jean
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Schmeiser, Christian
13321 Fakultät für Mathematik [Wien]
Type
Article accepté pour publication ou publié
Abstract (EN)
This paper is devoted to Fokker-Planck and linear kinetic equations with very weak confinement corresponding to a potential with an at most logarithmic growth and no integrable stationary state. Our goal is to understand how to measure the decay rates when the diffusion wins over the confinement although the potential diverges at infinity.