{
  "id": "1702.01718",
  "version": "v1",
  "published": "2017-02-06T17:28:02.000Z",
  "updated": "2017-02-06T17:28:02.000Z",
  "title": "Continuum limit of Follow-the-Leader models",
  "authors": [
    "Helge Holden",
    "Nils Henrik Risebro"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We offer a simple proof that the Follow-the-Leader model converges to the Lighthill--Whitham--Richards model for traffic flow when traffic becomes dense. The proof is based on techniques used in the analysis of numerical schemes for conservation laws, and the equivalence of weak entropy solutions of conservation laws in the Lagrangian and Eulerian formulation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-06T17:28:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L02",
      "35Q35",
      "82B21"
    ],
    "keywords": [
      "continuum limit",
      "conservation laws",
      "follow-the-leader model converges",
      "weak entropy solutions",
      "lighthill-whitham-richards model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}