Event

Franca Hoffmann, Caltech

Monday, November 27, 2017 16:00to17:00
Burnside Hall Room 920, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA

Title: Equilibria in energy landscapes with 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 homogeneous functionals and 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. Our goal is to understand better the asymptotic behavior of solutions in each of these regimes, starting with the fair-competition regime where attractive and repulsive forces are in balance. This is joint work with José A. Carrillo and Vincent Calvez.

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