6° Seminario Volterra: 17 aprile, 4pm @IAC


Speaker: Emanuela Radici (UnivAq)

CNR-IAC, Aula Primo Piano

Deterministic particle approximations for nonlocal transport equations and degenerate second order traffic models

In this talk we discuss a deterministic particle approach for a wide class of scalar nonlinear models, including first and second oder ones describing crowd dynamics. The congestion term appears in the equation in the form of a compactly supported nonlinear mobility function, thus making standard weak-type compactness arguments and uniqueness of weak solutions fail. We consider several generalizations of the deterministic Follow-theleader scheme, which can be interpreted as Lagrangian discretisations of the target pdes, and investigate the compactness properties of suitable approximations of the relevant macroscopic quantities. For first order nonlocal transport models we show that such schemes provide in the many particle limit, and under mild assumptions on the potentials, the unique entropy solution in the sense of Kruˇzkov. We then consider second order traffic models in which the drivers’ reaction time depends on both the inertia and a congestion term. In this case, we obtain in the many particle limit suitable weak-type solutions of a degenerate pressurless Euler-type system and we recover the first order model with nonlinear mobility in the joint many-particle/ vanishing-inertia regime.

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