On a stochastic approach to a diffusion-growth-fragmentation equation in a chemostat
Catégorie d'évènement : Groupe de travail Probabilités et Statistique Date/heure : 19 janvier 2023 10:45-11:45 Lieu : Salle de conférences Nancy Oratrice ou orateur : Josué Tchouanti (Neuromod Institute, Université Côte-d’Azur) Résumé :Attention: changement d’horaire: horaire du seminaire. Une visio sera mise en place.
The growth-fragmentation equation is a well-known model for modelling the dynamics of a size-structured
bacterial population. In this presentation, we will focus on a non-linear version of this equation with a
diffusion term and coupled to the dynamics of a resource. This new model describes the growth of a
bacterial population in a continuous medium, and structured according to the expression of a protein
involved in the individual metabolism. We will establish the existence of the solution by showing that
this model can be seen as the large population limit of a stochastic individual-based model. We will
then show the uniqueness of this solution and some qualitative results thanks to the properties of the
semi-group of the stochastic process that describes the protein expression of a typical individual in the
population.
L’orateur est invité BIGS.