The PhD fellow will study macroscopic pedestrian traffic flow models consisting in hyperbolic PDEs from an analytical and numerical point of view.
In particular, the PhD fellow will investigate the analytical properties of the solutions such as their existence, uniqueness and long-time behavior, as well as the construction of numerical schemes for efficiently computing solutions.
The considered equations do not fit the hypotheses of the results available in the literature, and need the construction of
new "ad hoc" methods.
Numerical simulations will provide a useful support for determining which models can capture the targeted features.
In a second time, the PhD fellow will address the problem of combining microscopic and macroscopic methods in hybrid models in which the individuality of each "particle" is maintained. He/she will analyze the well-posedness such models. This would allow to model individual trajectories starting from the global dynamics, and to treat related control problems.