Laboratoire de Mathématiques de Besançon - UMR 6623 CNRS

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1er octobre 2020: 1 événement

  • Séminaire d’Analyse Numérique et Calcul Scientifique

    Jeudi 1er octobre 11:00-12:00 - Hugo MARTIN - INSERM et Paris Sud

    Séminaire ANCS : Hugo MARTIN

    Résumé : Periodic asymptotic dynamics of the measure solutions to a growth-fragmentation equation in a critical case
    In the last years, measure solutions to PDE, in particular to model populations, have drawn much attention. The talk will be devoted to the presentation of a recent, unusual result in this field, that we obtained with Pierre Gabriel.
    First, I will expose some wellposedness and asymptotic results for two famous population equations in the L^p and measure frameworks, and explain the critical case that interested us. Then, I will define the notion of solution we used, and if needed, recall some basic definitions about semigroups.
    Moving to the proof itself, I will present the main steps of the proof of the wellposedness of the problem, that relies on a duality relation used to build a solution expressed as a semigroup acting on an initial measure. Then, I will go a little more into details of the demonstration of the asymptotic behaviour, namely a convergence in total variation norm toward an oscillating measure.

    Lieu : Salle 316Bbis - Laboratoire de Mathématiques
    Université de Franche-Comté
    16 route de Gray
    25030 Besançon CEDEX

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