Young Researchers Workshop:
Kinetic and macroscopic models for complex systems

The diffusive aggregation equation

José Alfredo Cañizo

University of Birmingham


We consider the aggregation equation, used in several collective behavior models, with an added diffusion term and (mostly) a smooth potential. When the potential is small enough one can show then that the asymptotic behavior of the equation is similar to that of the heat equation. Several questions are open in the case of a large (still smooth) potential, or potentials with singularities.