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Séminaire du LJLL : I. Kim
27 mars 2015 — 14h00
Inwon Kim (Université de Californie à Los Angeles)
Congested crowd motion and quasi-static evolution
Abstract
In this talk we investigate the relationship between a quasi-static evolution and a transport equation with a drift potential, where the density is transported with a constraint on its maximum. The latter model, in a simplified setting, describes the congested crowd motion with a density constraint. When the drift potential has positive laplacian, the crowd density is likely to aggregate, and thus if the initial density starts as a patch (i.e. if it is a characteristic function of some set) then it is expected that the density evolves as a patch. We show that the evolving patch satisfies a Hele-Shaw type equation. If time permits, we will also discuss some preliminary results on the case of interaction potential arising from aggregation equation.