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H 1 Using Harris’s theorem to show convergence to equilibrium for kinetic equations

Auteurs : Evans, Josephine (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : I will discuss a joint work with Jose Canizo, Cao Chuqi and Havva Yolda. I will introduce Harris’s theorem which is a classical theorem from the study of Markov Processes. Then I will discuss how to use this to show convergence to equilibrium for some spatially inhomogeneous kinetic equations involving jumps including jump processes which approximate diffusion or fractional diffusion in velocity. This is the situation in which the tools of ’Hypocoercivity’ are used. I will discuss the connections to hypocoercivity theory and possible advantages and disadvantages of approaches via Harris’s theorem.

    Keywords : Harris’s theorem; convergence to equilibrium; kinetic equation; jump process; hypocoercivity

    Codes MSC :
    35B40 - Asymptotic behavior of solutions of PDE
    35Q20 - Boltzmann equations
    60J75 - Jump processes
    82C40 - Kinetic theory of gases

      Informations sur la Vidéo

      Langue : Anglais
      Date de captation : 13/12/2018
      Collection : Research talks ; Partial Differential Equations ; Probability and Statistics
      Format : MP4
      Domaine : PDE ; Probability & Statistics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2018-12-13_Evans.mp4

    Informations sur la rencontre

    Nom de la rencontre : Non standard diffusions in fluids, kinetic equations and probability / Diffusions non standards en mécanique des fluides, équations cinétiques et probabilités
    Organisateurs de la rencontre : Imbert, Cyril ; Mouhot, Clément ; Tristani, Isabelle
    Dates : 10/12/2018 - 14/12/2018
    Année de la rencontre : 2018
    URL Congrès : https://conferences.cirm-math.fr/1862.html

    Citation Data

    DOI : 10.24350/CIRM.V.19483403
    Cite this video as: Evans, Josephine (2018). Using Harris’s theorem to show convergence to equilibrium for kinetic equations. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19483403
    URI : http://dx.doi.org/10.24350/CIRM.V.19483403

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