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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 )

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 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 hyperboliquesOrganisateurs de la rencontre : Caputo, Pietro ; Fathi, Max ; Guillin, Arnaud ; Reygner, JulienDates : 14/10/2019 - 18/10/2019 Année de la rencontre : 2019 URL Congrès : https://conferences.cirm-math.fr/2083.htmlCitation 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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