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

Université Paris Dauphine
Institut Universitaire de France

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	643-680
Number of pages	38
Journal	Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
Volume	35
Issue number	4
DOIs	https://doi.org/10.4171/RLM/1055
Publication status	Published - 1 Jan 2024

Keywords

Kinetic Fokker–Planck equation
hypocoercivity
long-time asymptotic behavior
ultracontractivity

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10.4171/RLM/1055

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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. In: Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni. 2024 ; Vol. 35, No. 4. pp. 643-680.

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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, no. 4, pp. 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.
In: Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, Vol. 35, No. 4, 01.01.2024, p. 643-680.

Research output: Contribution to journal › Article › peer-review

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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 Jan 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

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