Stability estimates for non-local scalar conservation laws

TL;DR

This paper establishes the stability of solutions to non-local scalar conservation laws, crucial for traffic modeling, by deriving estimates on how solutions depend on various parameters, supported by numerical simulations.

Contribution

It provides the first stability estimates for entropy solutions of non-local scalar conservation laws with applications to traffic flow.

Findings

Solutions depend continuously on kernel, speed, and initial data.

Stability is proven using the doubling of variables technique.

Numerical simulations illustrate the theoretical dependencies.

Abstract

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 technique. We finally provide some numerical simulations illustrating the dependencies above for some cost functionals derived from traffic flow applications.