arXiv subjects

Claudia Nocita

Publications and source records attributed to Claudia Nocita.

4 recordsLinked to original sources

arXiv2026

General Periodic Conservation Laws Motivated by Traffic Modeling

This paper deals with the well-posedness, in the spatially periodic setting, of a mixed system of nonlocal-local conservation laws modeling traffic flow where autonomous vehicles --- informed on traffic conditions over long distances --- interact with human-driven bulk traffic. We also provide a comprehensive well-posedness theory in the periodic framework separately for general local conservation laws and for systems of nonlocal conservation laws, together with a priori total variation bounds and stability estimates.

math.AP↗

arXiv2025

Coexisting Automated and Human-Driven Vehicles: Well-Posedness of a Mixed Nonlocal-Local Traffic Model

We present a macroscopic traffic flow model where standard vehicles coexist with vehicles informed on the traffic distribution. The resulting mixed nonlocal-local integro-differential PDEs is proved to generate a locally Lipschitz continuous semigroup whose orbits are uniquely characterized as solutions to the system, according to a natural definition of solution. The norms and function spaces adopted are intrinsic to the different nature of the equations.

math.AP↗

arXiv2025

Control of Conservation Laws in the Nonlocal-to-Local Limit

We analyze a class of control problems where the initial datum acts as a control and the state is given by the entropy solution of (local) conservation laws by a nonlocal-to-local limiting strategy. In particular we characterize the limit up to subsequence of minimizers to nonlocal control problems as minimizer of the corresponding local ones. Moreover, we also prove an analogous result at a discrete level by means of a Eulerian-Lagrangian scheme.

math.OC↗

arXiv2025

General Stability Estimates in NonLocal Traffic Models for Several Populations

We prove global existence, uniqueness and $\L1$ stability of solutions to general systems of nonlocal conservation laws modeling multiclass vehicular traffic. Each class follows its own speed law and has specific effects on the other classes' speeds. Moreover, general explicit dependencies of the speed laws on space and time are allowed. Solutions are proved to depend continuously -- in suitable norms -- on all terms appearing in the equations, as well as on the initial data. Numerical simulations show the relevance and the effects of the nonlocal terms.

math.AP↗