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Deterministic particle approximations of local and nonlocal transport equations

Banff International Research Station for Mathematical Innovation and Discovery

Nonlinear convection and nonlocal aggregation equations are known to feature a "formal" gradient flow structure in presence of a "nonlinear mobility", in terms of the generalized Wasserstein distance "à la" Dolbeault-Nazaret-Savaré. Such a structure is inherited by the discrete Lagrangian approximations of those equations in a quite natural way in one space dimension, and this simple remark allows to formulate a discrete-to-continuum "many particle" approximation. I will describe some recent results in this direction, which include the discrete (deterministic) particle approximation for scalar conservation laws and (more recently) a large class of nonlocal aggregation equations as main examples. The results are in collaboration with M. D. Rosini (Ferrara), S. Fagioli and E. Radici (L'Aquila).

Mathematics; Partial differential equations; Statistical mechanics, structure of matter

video/mp4

Author affiliation: University of L'Aquila

2018-10-10

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/67432

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/