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

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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.

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Authors and Affiliations

  1. DISIM, University of L’Aquila, Via Vetoio, 67100, L’Aquila, Italy

    F. A. Chiarello

  2. GIMNAP-Departamento de Matemáticas, Universidad del Bío-Bío, Concepción, Chile

    H. D. Contreras & L. M. Villada

  3. CI£MA, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    L. M. Villada

Authors
  1. F. A. Chiarello
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  2. H. D. Contreras
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  3. L. M. Villada
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Correspondence to F. A. Chiarello.

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HDC and LMV are supported by project MATH-Amsud 22-MATH-05 “NOTION: NOn-local conservaTION laws for engineering, biological and epidemiological applications: theoretical and numerical” and by INRIA Associated Team “Efficient numerical schemes for non-local transport phenomena” (NOLOCO; 2018–2022). Additionally, LMV was partially supported by ANID-Chile through the project Centro de Modelamiento Matemático (AFB170001) of the PIA Program: Concurso Apoyo a Centros Científicos y Tecnológicos de Excelencia con Financiamiento Basal and by Fondecyt project 1181511. HDC was partially supported by the National Agency for Research and Development, ANID-Chile through Scholarship Program, Doctorado Becas Chile 2021, 21210826.

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Chiarello, F.A., Contreras, H.D. & Villada, L.M. Existence of entropy weak solutions for 1D non-local traffic models with space-discontinuous flux. J Eng Math 141, 9 (2023). https://doi.org/10.1007/s10665-023-10284-5

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  • DOI: https://doi.org/10.1007/s10665-023-10284-5

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