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Large time asymptotics for evolution equations with mean field couplings

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Virtualconference
Auteurs : Dolbeault, Jean (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : This lecture is devoted to the characterization of convergence rates in some simple equations with mean field nonlinear couplings, like the Keller-Segel and Nernst-Planck systems, Cucker-Smale type models, and the Vlasov-Poisson-Fokker-Planck equation. The key point is the use of Lyapunov functionals adapted to the nonlinear version of the model to produce a functional framework adapted to the asymptotic regime and the corresponding spectral analysis.

Keywords : hypocoercivity; large-time behaviour; mean-field models; drift-diffusion equations; Keller-Segel; Cucker-Smale; Vlasov-Poisson-Fokker-Planck; rate of convergence

Codes MSC :
35H10 - Hypoelliptic equations
35K55 - Nonlinear parabolic equations
35K65 - Parabolic equations of degenerate type
35P15 - Estimation of eigenvalues and upper and lower bounds for PD operators
46E35 - Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
47G20 - Integro-differential operators, See also {45J05, 45K05}
76P05 - Rarefied gas flows, Boltzmann equation, See also {82B40, 82C40, 82D05}
82C21 - Dynamic continuum models (systems of particles, etc.)
82C40 - Kinetic theory of gases
82D10 - Plasmas
82D37 - semiconductors
35Q84 - Fokker-Planck equations
35Q70 - PDEs in connection with mechanics of particles and systems
35R09 - Integro-partial differential equations

Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Jean_DOLBEAULT.pdf

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 09/04/2021
    Date de captation : 25/03/2021
    Sous collection : Research talks
    arXiv category : Analysis of PDEs
    Domaine : Analysis and its Applications ; PDE ; Mathematical Physics
    Format : MP4 (.mp4) - HD
    Durée : 00:37:25
    Audience : Researchers
    Download : https://videos.cirm-math.fr/2021-03-25_Dolbeaut.mp4

Informations sur la Rencontre

Nom de la rencontre : Jean Morlet Chair 2021- Conference: Kinetic Equations: From Modeling Computation to Analysis / Chaire Jean-Morlet 2021 - Conférence : Equations cinétiques : Modélisation, Simulation et Analyse
Organisateurs de la rencontre : Bostan, Mihaï ; Jin, Shi ; Mehrenberger, Michel ; Montibeller, Celine
Dates : 22/03/2021 - 26/03/2021
Année de la rencontre : 2021
URL Congrès : https://www.chairejeanmorlet.com/2355.html

Données de citation

DOI : 10.24350/CIRM.V.19733603
Citer cette vidéo: Dolbeault, Jean (2021). Large time asymptotics for evolution equations with mean field couplings. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19733603
URI : http://dx.doi.org/10.24350/CIRM.V.19733603

Voir aussi

Bibliographie

  • ADDALA, Lanoir, DOLBEAULT, Jean, LI, Xingyu, et al. L2-Hypocoercivity and large time asymptotics of the linearized Vlasov-Poisson-Fokker-Planck system. arXiv preprint arXiv:1909.12762, 2019. - https://arxiv.org/abs/1909.12762

  • ARNOLD, Anton, DOLBEAULT, Jean, SCHMEISER, Christian, et al. Sharpening of decay rates in Fourier based hypocoercivity methods. arXiv preprint arXiv:2012.09103, 2020. - https://arxiv.org/abs/2012.09103

  • DOLBEAULT, Jean et LI, Xingyu. φ-entropies: Convexity, coercivity and hypocoercivity for Fokker–Planck and kinetic Fokker–Planck equations. Mathematical Models and Methods in Applied Sciences, 2018, vol. 28, no 13, p. 2637-2666. - https://arxiv.org/abs/1712.09897

  • LI, Xingyu. Asymptotic behavior of Nernst-Planck equation. arXiv preprint arXiv:1910.04477, 2019. - https://arxiv.org/abs/1910.04477

  • LI, Xingyu. Flocking: Phase transition and asymptotic behaviour. arXiv preprint arXiv:1906.07517, 2019. - https://arxiv.org/abs/1906.07517



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