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Diffusion and kinetic transport with very weak confinement

Bouin, Emeric; Dolbeault, Jean; Schmeiser, Christian (2020), Diffusion and kinetic transport with very weak confinement, Kinetic & Related Models, 13, 2, p. 345-371. 10.3934/krm.2020012

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Type
Article accepté pour publication ou publié
Date
2020
Journal name
Kinetic & Related Models
Volume
13
Number
2
Publisher
AIMS - American Institute of Mathematical Sciences
Pages
345-371
Publication identifier
Metadata
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Author(s)
Bouin, Emeric
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Dolbeault, Jean cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Schmeiser, Christian
Fakultät für Mathematik [Wien]
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.
Subjects / Keywords
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