Laboratoire de Mathématiques de Besançon - UMR 6623 CNRS

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26 avril 2021: 1 événement

  • Planning des séminaires 2020-2021

    Lundi 26 avril 11:00-12:00 - Benedetta Cavalli - Université de Zurich

    Séminaire PS : A probabilistic view on the long-time behaviour of growth-fragmentation equations with bounded fragmentation rates

    Résumé : The growth-fragmentation equation models systems of particles that grow and reproduce as time passes. An important question concerns the asymptotic behaviour of its solutions. This question has traditionally been addressed using analytic techniques such as entropy methods or splitting of operators.
    Bertoin and Watson (2018) developed a probabilistic approach relying on the Feynman-Kac formula, that enabled them to answer to this question in the case in which the growth rate is sublinear and the mass is conserved at fragmentation events. This assumption on the growth ensures that microscopic particles remain microscopic.
    In this talk, we present a recent work of the speaker, in which we go further in the analysis, assuming bounded fragmentations and allowing arbitrarily small particles to reach macroscopic mass in finite time. Moreover, we drop the hypothesis of conservation of mass when a fragmentation occurs. With the Feynman-Kac approach, we establish necessary and sufficient conditions on the coefficients of the equation that ensure the so-called Malthusian behaviour with exponential speed of convergence to the asymptotic profile. Furthermore, we provide an explicit expression of the latter.

    En savoir plus : Planning des séminaires 2020-2021