CRM: Centro De Giorgi
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Recent Trends in Nonlinear Diffusion

Discrete and continuous swarming models

speaker: Jesus Rosado (UCLA Department of Mathematics)

abstract: We study at particle and kinetic level models for collective behavior. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and selfpropulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models. In general it is difficult to study analytically the asymptotic behavior of solutions to this models, but numerical simulations can give us a hint about what to expect.

Fri 6 Jul, 9:00 - 10:00, Aula Dini
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