Partial Differential Equations. – The Kinetic Fokker–Planck equation in a domain: Ultracontractivity, hypocoercivity, and long-time asymptotic behavior

Kleber Carrapatoso; Stéphane Mischler

doi:10.4171/RLM/1055

Partial Differential Equations. – The Kinetic Fokker–Planck equation in a domain: Ultracontractivity, hypocoercivity, and long-time asymptotic behavior

Kleber Carrapatoso
, Stéphane Mischler

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We consider the Kinetic Fokker–Planck (FKP) equation in a domain with Maxwell reflection condition on the boundary. We establish the ultracontractivity of the associated semigroup and the hypocoercivity of the associated operator. We deduce the convergence with the constructive rate of the solution to the KFP equation towards the stationary state with the same mass as the initial datum.

langue originale	Anglais
Pages (de - à)	643-680
Nombre de pages	38
journal	Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
Volume	35
Numéro de publication	4
Les DOIs	https://doi.org/10.4171/RLM/1055
état	Publié - 1 janv. 2024

Accès au document

10.4171/RLM/1055

Autres fichiers et liens

Lien vers la publication dans Scopus

Contient cette citation

Carrapatoso, K., & Mischler, S. (2024). Partial Differential Equations. – The Kinetic Fokker–Planck equation in a domain: Ultracontractivity, hypocoercivity, and long-time asymptotic behavior. Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, 35(4), 643-680. https://doi.org/10.4171/RLM/1055

Carrapatoso, Kleber ; Mischler, Stéphane. / Partial Differential Equations. – The Kinetic Fokker–Planck equation in a domain : Ultracontractivity, hypocoercivity, and long-time asymptotic behavior. Dans: Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni. 2024 ; Vol 35, Numéro 4. p. 643-680.

@article{6f765afa9bb94359af02cd709493eaac,

title = "Partial Differential Equations. – The Kinetic Fokker–Planck equation in a domain: Ultracontractivity, hypocoercivity, and long-time asymptotic behavior",

abstract = "We consider the Kinetic Fokker–Planck (FKP) equation in a domain with Maxwell reflection condition on the boundary. We establish the ultracontractivity of the associated semigroup and the hypocoercivity of the associated operator. We deduce the convergence with the constructive rate of the solution to the KFP equation towards the stationary state with the same mass as the initial datum.",

keywords = "Kinetic Fokker–Planck equation, hypocoercivity, long-time asymptotic behavior, ultracontractivity",

author = "Kleber Carrapatoso and St{\'e}phane Mischler",

note = "Publisher Copyright: {\textcopyright} 2025 Accademia Nazionale dei Lincei.",

year = "2024",

month = jan,

day = "1",

doi = "10.4171/RLM/1055",

language = "English",

volume = "35",

pages = "643--680",

journal = "Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni",

issn = "1120-6330",

number = "4",

}

Carrapatoso, K & Mischler, S 2024, 'Partial Differential Equations. – The Kinetic Fokker–Planck equation in a domain: Ultracontractivity, hypocoercivity, and long-time asymptotic behavior', Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, VOL. 35, Numéro 4, p. 643-680. https://doi.org/10.4171/RLM/1055

Partial Differential Equations. – The Kinetic Fokker–Planck equation in a domain: Ultracontractivity, hypocoercivity, and long-time asymptotic behavior. / Carrapatoso, Kleber; Mischler, Stéphane.
Dans: Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, Vol 35, Numéro 4, 01.01.2024, p. 643-680.

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

TY - JOUR

T1 - Partial Differential Equations. – The Kinetic Fokker–Planck equation in a domain

T2 - Ultracontractivity, hypocoercivity, and long-time asymptotic behavior

AU - Carrapatoso, Kleber

AU - Mischler, Stéphane

PY - 2024/1/1

Y1 - 2024/1/1

N2 - We consider the Kinetic Fokker–Planck (FKP) equation in a domain with Maxwell reflection condition on the boundary. We establish the ultracontractivity of the associated semigroup and the hypocoercivity of the associated operator. We deduce the convergence with the constructive rate of the solution to the KFP equation towards the stationary state with the same mass as the initial datum.

AB - We consider the Kinetic Fokker–Planck (FKP) equation in a domain with Maxwell reflection condition on the boundary. We establish the ultracontractivity of the associated semigroup and the hypocoercivity of the associated operator. We deduce the convergence with the constructive rate of the solution to the KFP equation towards the stationary state with the same mass as the initial datum.

KW - Kinetic Fokker–Planck equation

KW - hypocoercivity

KW - long-time asymptotic behavior

KW - ultracontractivity

UR - https://www.scopus.com/pages/publications/105011154194

U2 - 10.4171/RLM/1055

DO - 10.4171/RLM/1055

M3 - Article

AN - SCOPUS:105011154194

SN - 1120-6330

VL - 35

SP - 643

EP - 680

JO - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni

JF - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni

IS - 4

ER -

Carrapatoso K, Mischler S. Partial Differential Equations. – The Kinetic Fokker–Planck equation in a domain: Ultracontractivity, hypocoercivity, and long-time asymptotic behavior. Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni. 2024 janv. 1;35(4):643-680. doi: 10.4171/RLM/1055

Partial Differential Equations. – The Kinetic Fokker–Planck equation in a domain: Ultracontractivity, hypocoercivity, and long-time asymptotic behavior

Résumé

Accès au document

Autres fichiers et liens

Empreinte digitale

Contient cette citation