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Informal Systems Seminar (ISS), Centre for Intelligent Machines (CIM) and Groupe d'Etudes et de Recherche en Analyse des Decisions (GERAD)

Systems of Evolution Equations Coupled Through Optimal Transport and Application to Urban Planning


Maxime Laborde
Maxime Laborde McGill University

February 28, 2020 at  10:30 AM
McConnell Engineering Room 437

In 1998, Jordan, Kinderlehrer and Otto introduced gradient flows in the Wasserstein space to prove existence (and uniqueness) of parabolic equations under very weak assumptions on the initial condition. In this talk, we show that this method provides a good framework to study systems of parabolic equations coupled via optimal transport problems. A simple example consists in solving two equations coupled through the solution to the very degenerate Monge-Ampère equation which can appear for example in dynamical urban planning model.