Non-local traffic flow models with time delay: well-posedness and numerical approximation
<|reference_start|>Non-local traffic flow models with time delay: well-posedness and numerical approximation: We prove the well-posedness of weak entropy solutions of a scalar non-local traffic flow model with time delay. Existence is obtained by convergence of finite volume approximate solutions constructed by Lax-Friedrich and Hilliges-Weidlich schemes, while the L1 stability with respect to the initial data and the delay parameter relies on a Kruzkov-type doubling of variable technique.Numerical tests are provided to illustrate the efficiency of the proposed schemes, as well as the solution dependence on the delay and look-ahead parameters.<|reference_end|>
@article{ciaramaglia2024non-local,
    title={Non-local traffic flow models with time delay: well-posedness and
  numerical approximation},
    author={Ilaria Ciaramaglia (ACUMES, LJAD, UniCA), Paola Goatin (ACUMES, JAD,
  UniCA), Gabriella Puppo (UNIROMA)},
    journal={arXiv preprint arXiv:2404.10368},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.10368},
    primaryClass={math.AP cs.NA math.NA}
}