香蕉视频

Title : Systems of evolution equations coupled through optimal transport and application to urban planning

Abstract :

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-Amp猫re equation which can appear for example in dynamical urban planning model.