General Stability Estimates in NonLocal Traffic Models for Several Populations

TL;DR

This paper establishes the global existence, uniqueness, and stability of solutions for nonlocal traffic models involving multiple vehicle classes, incorporating complex speed dependencies and validated through numerical simulations.

Contribution

It introduces a comprehensive framework for analyzing multiclass nonlocal traffic models with explicit space-time dependencies, ensuring stability and continuous dependence on data.

Findings

Proved global existence and uniqueness of solutions.

Established L1 stability of solutions.

Numerical simulations demonstrate the impact of nonlocal terms.

Abstract

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.