Variational approximation of “entropic” deterministic particles evolution

par Emanuela Radici (Univ. L'Aquila)

mercredi 2 juil. 2025, 10:00 → 11:30 Europe/Paris

séminaire 1 (Braconnier)

In this talk we consider a class of scalar nonlinear models describing crowd dynamics. The congestion term appears in the transport equation in the form of a compactly supported nonlinear mobility function, thus making standard weak-type compactness arguments and uniqueness of weak solutions fail. In most cases well-posedness can be restored within the subclass of Kruzkov entropy solutions of the target pde and such entropic solution, at least in the case of one dimensional evolutions, can be obtained via deterministic many particle limit of suitable generalisations of the Follow-the-leader scheme. Relying on the formal gradient flow structure of the macroscopic transport equation, we discuss how this structure is inherited by the particle system in suitable “discrete” metric framework and how it can be exploited to approximate the particles evolution in case of monotone external potentials