CHIARELLO , Felisia Angela

We give an overview of mathematical traffic flow models with non-local velocity. More precisely, we consider conservation laws with flux functions depending on an integral evaluation of the density of vehicles through a convolution product. We summarize the analytical results recently obtained for this kind of models and we provide some...

In this thesis, we provide mathematical traffic flow models with non-local fluxes and adapted numerical schemes to compute approximate solutions to such kind of equations. More precisely, we consider flux functions depending on an integral evaluation of the conserved variables through a convolution product. First of all, we prove the...

We present a non-local model describing the dynamics of two groups of agents moving in opposite directions. The model consists of a 2 × 2 system of conservation laws with non-local fluxes, coupled in the speed functions. We prove local in time existence of weak solutions and present some numerical tests illustrating their behaviour.

We prove the existence for small times of weak solutions for a class of non-local systems in one space dimension, arising in traffic modeling. We approximate the problem by a Godunov type numerical scheme and we provide uniform L ∞ and BV estimates for the sequence of approximate solutions. We finally present some numerical simulations...

We prove the well-posedness of entropy weak solutions for a class of scalar conservation laws with non-local flux arising in traffic modeling. We approximate the problem by a Lax-Friedrichs scheme and we provide L ∞ and BV estimates for the sequence of approximate solutions. Stability with respect to the initial data is obtained from the...

We prove the stability of entropy weak solutions of a class of scalar conservation laws with non-local flux arising in traffic modelling. We obtain an estimate of the dependence of the solution with respect to the kernel function, the speed and the initial datum. Stability is obtained from the entropy condition through doubling of variable...

This paper focuses on the numerical approximation of a class of non-local systems of conservation laws in one space dimension, arising in traffic modeling, proposed by [F. A. Chiarello and P. Goatin. Non-local multi-class traffic flow models. Networks and Heterogeneous Media, to appear, Aug. 2018]. We present the multi-class version of the...

This paper focuses on the numerical approximation of the solutions of a class of non-local systems in one space dimension, arising in traffic modeling. We propose alternative simple schemes by splitting the non-local conservation laws into two different equations, namely, the Lagrangian and the remap steps. We provide some properties and...

We introduce a Follow-the-Leader approximation of a non-local generalized Aw-Rascle-Zhang (GARZ) model for traffic flow. We prove the convergence to weak solutions of the corresponding macroscopic equations deriving $L ∞$ and BV estimates. We also provide numerical simulations illustrating the micro-macro convergence and we investigate...

We present a model for a class of non-local conservation laws arising in traffic flow modeling at road junctions. Instead of a single velocity function for the whole road, we consider two different road segments, which may differ for their speed law and number of lanes (hence their maximal vehicle density). We use an upwind type numerical...