Caltech/UCLA/USC Joint Analysis Seminar
In this talk I am going to analyze the compressible dissipative hydrodynamic model of crowd motion or of granular flow. The model resembles the famous Aw-Rascle model of traffic, except that the difference between the actual and the desired velocities (the offset function) is a gradient of the density function, and not a scalar. This modification gives rise to a dissipation term in the momentum equation that vanishes when the density is equal to zero.
I will compare the dissipative Aw-Rascle system with the compressible Euler and compressible Navier-Stokes equations, and back it up with two existence and ill-posedness results. In the last part of my talk I will explain the proof of conjecture made by Lefebvre-Lepot and Maury, that the hard congestion limit of this system (with singular offset function) leads to congested compressible/incompressible Euler equations.