One-dimensional diffusion-aggregation models with non convex interaction potentials.
by
Marco Di Francesco
University of L'Aquila
Coauthors: Martin Burger (University of Muenster).

Diffusion-aggregation models from population biology can be interpreted as gradient flows with respect to the Euclidean Wasserstein distance (cf. the works of Ambrosio-Gigli-Savaré or Carrillo-McCann-Villani).

We first present an improved existence theory in some special cases, in 1d, where the interaction potential need not be globally convex.

Then, we prove that models without diffusion enjoy asymptotically stable measure valued equilibria, with various large time behaviors depending on the properties of the interaction potential.

Finally, we prove existence of stationary compactly supported solutions for the model with (small) quadratic diffusion.

Date received: July 25, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavl-62.