06/12/2023, 16:00 — 17:00 — Online
Alessia Nota, University of L'Aquila
On the Smoluchowski equation for aggregation phenomena: stationary non-equilibrium solutions
Smoluchowski’s coagulation equation, an integro-differential equation of kinetic type, is a classical mean-field model for mass aggregation phenomena. The solutions of the equation exhibit rich behavior depending on the rate of coagulation considered, such as gelation (formation of particles with infinite mass in finite time) or self-similarity (preservation of the shape over time). In this talk I will first discuss some fundamental properties of the Smoluchowski equation. I will then present some recent results on the problem of existence or non-existence of stationary solutions, both for single and multi-component systems, under non-equilibrium conditions which are induced by the addition of a source term for small cluster sizes. The most striking feature of these stationary solutions is that, whenever they exist, the solutions to multi-component systems exhibit an unusual “spontaneous localization” phenomenon: they localize along a line in the composition space as the total size of the particles increase. This localization is a universal property of multicomponent systems and it has also been recently proved to occur in time dependent solutions to mass conserving coagulation equations.
(Based on joint works with M. Ferreira, J. Lukkarinen and J. Velázquez)
