In this session various kinds of transport problems and models will be considered. This includes optimal transport theory, transport and kinetic equations, and other PDEs modeling fluid mechanics or vehicle and pedestrian motion. Several models where individuals react to the surrounding density of other individuals can be considered: in the static framework we will see the connection between Wardrop equilibria and degenerate elliptic PDEs; in dynamics, we will see a compressible Euler-type equation from a hyperbolic limit of the kinetic description of the Cucker-Smale model, or equations with non-local flux, displaying finite acceleration of vehicles through Lipschitz bounds on the mean velocity. Other evolution PDEs will be considered, such as cross-diffusion, in terms of gradient flow (or asymptotic gradient flow near equilibria), and problems related to the Euler equation and other non-linear hyperbolic PDE (the aggregation equation, for instance).
Speakers
Mark Peletier
Technische Universiteit Eindhoven
Upscaling the dynamics of dislocations
Thursday, 27 April, 16:30-17:15. Room Pi i Sunyer
Marie-Therese Wolfram
University of Warwick
Analysis of a cross-diffusion model with excluded volume effects and asymptotic gradient flows
Thursday, 27 April, 17:20-18:05. Room Pi i Sunyer
Juan Soler
Universidad de Granada
Exploring new solutions to the incompressible Euler equations
Thursday, 27 April, 18:10-18:55. Room Pi i Sunyer
Filippo Santambrogio
Université Paris-Sud
Congested transport problems and equilibria
Friday, 28 April, 16:30-17:15. Room Pi i Sunyer
Paola Goatin
Institut National de Recherche en Informatique et en Automatique, Sophia Antipolis
Non-local conservation laws arising in traffic modeling
Friday, 28 April, 17:20-18:05. Room Pi i Sunyer
José A. Carrillo
Imperial College London
Minimizing interaction energies
Friday, 28 April, 18:10-18:55. Room Pi i Sunyer
Organisers
Joan Orobitg
Universitat Autònoma de Barcelona
Filippo Santambrogio
Université Paris-Sud
