Micro to macro passage for growth-fragmentation equations with short-range interactions

Sophie Hecht (Sorbonne U, Paris)

Nov 22. 2022, 14:45 — 15:30

We investigate the micro to macro passage for a system of spherical particles of different radii interacting via short-range repulsion and undergoing growth and division. We first perform the mean field limit scaling limit considering a large number of particles and rigoursly show that, under appropriate assumption, the resulting mesoscopic equation is non-local non-linear diffusion equation for the interaction part, combined with a growth fragmentation equation, describing the evolution of the particle distribution structured in time, space and radius. We then rigorously show that in a scaling limit, considering the interaction potential approaches the Dirac delta distribution, the mesocopic equation converge toward a non-linear microscopic equation with linear source terms. The three models are compared with numerically to show that they are in good agreement and simulations are used to explore the different behaviours of the model. 

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Mathematical Methods for the Study of Self-organization in the Biological Sciences (Thematic Programme)
Pierre Degond (IMT)
Marie Doumic (Sorbonne U, Paris)
Anna Kicheva (ISTA, Klosterneuburg)
Sara Merino-Aceituno (U of Vienna)
Christian Schmeiser (U of Vienna)