Existence of entropy weak solutions for 1D non-local traffic models with space-discontinuous flux

TL;DR

This paper proves the existence and uniqueness of entropy weak solutions for a 1D non-local traffic flow model with spatial discontinuities, supported by numerical simulations and analysis of the zero-kernel limit.

Contribution

It introduces a novel approach to handle non-local flux with spatial discontinuities in traffic models, establishing well-posedness and numerical validation.

Findings

Existence and uniqueness of entropy weak solutions are proven.

Numerical simulations support theoretical results.

The zero-kernel limit of the model is numerically examined.

Abstract

We study a 1D scalar conservation law whose non-local flux has a single spatial discontinuity. This model is intended to describe traffic flow on a road with rough conditions. We approximate the problem through an upwind-type numerical scheme and provide compactness estimates for the sequence of approximate solutions. Then, we prove the existence and the uniqueness of entropy weak solutions. Numerical simulations corroborate the theoretical results and the limit model as the kernel support tends to zero is numerically investigated.