Iulia Cristian
University of Bonn, Bonn, Germany

In this talk, we investigate the long-time asymptotics of a coagulation model which describes the evolution of a system of particles characterized by their volume and surface area. The aggregation mechanism takes place in two stages: collision and fusion of particles. We assume the coagulation kernel has a weak dependence on the area variable.

We discover that the long-time analysis of the system is strictly related to the chosen fusion rate. We prove existence of self-similar profiles for some choices of the functions describing the fusion rate for which the particles have a shape that is close to spherical. On the other hand, for other fusion mechanisms, we show that the particle distribution describes a system of ramified-like particles.

Lastly, we talk about how we are able to recover the standard coagulation equation in the case of fast fusion.

This is joint work with J. J. L. Velázquez (University of Bonn).