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H 1 Exponential stability of BV solutions in a model of granular flow

Auteurs : Caravenna, Laura (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : We are concerned with the well-posedness of a model of granular flow that consists of a hyperbolic system of two balance laws in one-space dimension, which is linearly degenerate along two straight lines in the phase plane and genuinely nonlinear in the subdomains confined by such lines. After introducing the problem, I discuss recent results on the Lipschitz L1-continuous dependence of the entropy weak solutions on the initial data, with a Lipschitz constant that grows exponentially in time. Our analysis relies on the extension of a Lyapunov like functional and provides the first construction of a Lipschitz semigroup of entropy weak solutions to the regime of hyperbolic systems of balance laws (i) with characteristic families that are neither genuinely nonlinear nor linearly degenerate and (ii) initial data of arbitrarily large total variation.

    Keywords : balance laws; global large BV; granular flow; $L^{1}$-stability; weakly linearly; degenerate system

    Codes MSC :
    35L45 - Initial value problems for hyperbolic systems of first-order PDE
    35L65 - Conservation laws

    Ressources complémentaires :
    https://www.cirm-math.fr/RepOrga/2083/Slides/marsiglia_granular_flow_2019.pdf

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 04/11/2019
      Date de captation : 17/10/2019
      Collection : Research talks ; Analysis and its Applications ; Partial Differential Equations
      Format : MP4
      Durée : 00:53:49
      Domaine : Analysis and its Applications ; PDE
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-10-17_Caravenna.mp4

    Informations sur la rencontre

    Nom de la rencontre : PDE/Probability Interactions: Particle Systems, Hyperbolic Conservation Laws / Interactions EDP/Probabilités : systèmes de particules, lois de conservation hyperboliques
    Organisateurs de la rencontre : Caputo, Pietro ; Fathi, Max ; Guillin, Arnaud ; Reygner, Julien
    Dates : 14/10/2019 - 18/10/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/2083.html

    Citation Data

    DOI : 10.24350/CIRM.V.19569903
    Cite this video as: Caravenna, Laura (2019). Exponential stability of BV solutions in a model of granular flow. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19569903
    URI : http://dx.doi.org/10.24350/CIRM.V.19569903


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