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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium

Franca Hoffmann
Caltech
Title: Equilibria for nonlinear diffusion and nonlocal interaction

Abstract: We study interacting particles behaving according to a reaction-diffusion equation with nonlinear diffusion and nonlocal attractive interaction. This class of partial differential equations has a very nice gradient flow structure that allows us to make links to variations of well-known functional inequalities. Depending on the nonlinearity of the diffusion, the choice of interaction potential and the space dimensionality, we obtain different regimes. This talk will give an overview of recent advances in the fair-competition regime where repulsive and attractive forces are in balance, and the diffusion-dominated regime where the corresponding energy functional is non-homogeneous. These are joint works with Jose A. Carrillo, Vincent Calvez, Jean Dolbeault, Rupert Frank, Edoardo Mainini and Bruno Volzone.

Recording: http://mm.math.cmu.edu/recordings/cna/franca_hoffmann_small.mp4
Date: Thursday, March 8, 2018
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  Slepcev