arXiv subjects

Harold Deivi Contreras

Publications and source records attributed to Harold Deivi Contreras.

2 recordsLinked to original sources

arXiv2023

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

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.

math.AP↗

arXiv2023

Stability estimates for nonlocal balance laws arising in traffic modelling

This paper focuses on the proof of the stability of entropy weak solutions of a nonlocal balance law modeling vehicular traffic flow on a road with on- and off-ramps. The stability is obtained with respect to a kernel function in the source term. We get an estimate of the L1-dependence of the solution with respect to the initial datum, the on-ramp rate, the off-ramp rate and the mentioned kernel function. We also show numerical experiments in order to perform an optimization problem in traffic flow with on-ramps.

math.AP↗