On the Smoluchowski equation for aggregation phenomena: stationary non-equilibrium solutions

Nota Alessia, University of L'Aquila

In this talk I will first discuss some fundamental properties of the Smoluchowski’s coagulation equation, an integro-differential equation of kinetic type, which provides a mean-field description for mass aggregation phenomena. 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)

Area: CS57 - Statistical Mechanics and applications (Tobias Kuna)

Keywords: Smoluchowski’s equation; Coagulation dynamics; non-equilibrium; source term; stationary injection solutions; localization

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