Alessia Nota, "Kinetic equations for problems of particle aggregation"
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Europe/Rome
Ex-ISEF/Building-Room A (GSSI)
Ex-ISEF/Building-Room A
GSSI
20
Description
Title: Kinetic equations for problems of particle aggregation
Description: The phenomenon of coagulation (coalescence or aggregation) is the mechanism by which particles (clusters) grow, the underlying process being successive mergers. It can be observed in physical systems, e.g., aerosol and raindrop formation, smoke, sprays and galaxies, as well as in biological systems. The evolution of the particle size distribution is described at mesoscopic level by the Smoluschowki coagulation equation, an integro-differential equation of kinetic type, which provides a mean-field model of clustering dynamics. Coagulation equations are not only relevant from the point of view of applications; they are also fascinating due to the rich structure that solutions can display. Its solutions exhibit rich behavior depending on the structure of the kernel which gives the rate to each coagulation, such as the phase transition termed as gelation (giant particles appear in finite time) or self-similarity (preservation of the shape over time).
In this course we will review the basic properties of the Smoluchowski equation, explaining some of the main challenges in the analysis and discussing some of the fundamental results obtained in the literature in the last decades. Moreover, we will investigate the connection between the Smoluchowski coagulation equation and other classical kinetic equations, as well as the validation of the coagulation equation from suitable particle systems.
Preliminary Schedule (First Part in June):
Wednesday 4th June, 12:15--13:45 in Room A (Ex-ISEF)
Friday 6th June, 15:30--17:00 in Room A (Ex-ISEF)
Monday 16th June, 9:15--10.45 in Room A (Ex-ISEF)
Wednesday 18th June, 10:45--12:15 in Room A (Ex-ISEF)
Tuesday 24th June, 10.45--12:15 in Room A (Ex-ISEF)
Thursday 26th June, 10:45--12:15 in Room A (Ex-ISEF)
Friday 27th June, 15.30--17.00 in Room A (Ex-ISEF)
