{
  "abstract": "The paper is concerned with the homogenization of first-order, time-dependent Hamilton- Jacobi equations on a one-dimensional spatial domain with infinitely many junctions located at integer points. The Hamiltonian may be non-convex and exhibits discontinuities both in time and space: the set of time discontinuities may be dense in time, while the spatial discontinuities occur at infinitely many junctions that are discrete in space. This configu- ration arises naturally for example in the modeling of a infinite number of trafic lights on a single road and creates significant analytical challenges, in particular due to the absence of a standard viscosity solution theory adapted to this setting. To overcome this difficulty, we introduce a new notion of viscosity solution, called Lipschitz lattice viscosity solution, for which we prove a comparison principle. The Lipschitz regularity plays a crucial role in this definition and we then have to prove, under suitable structural assumptions, global Lipschitz estimates for the solutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Ali Assi"
    },
    {
      "name": "Nicolas Forcadel"
    },
    {
      "name": "Regis Monneau"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3b352phf9ngtq.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "3b352phf9ngtq",
  "issns": [],
  "landing_url": "https://hal.science/hal-05837643v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-ap"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05837643/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3b352phf9ngtq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "hal-05837643",
      "source": "hal",
      "url": "https://hal.science/hal-05837643v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ap",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Green Waves I: A PDE Approach to Homogenization of Lines of Traffic Lights (Preliminary version)",
  "title_text": "Green Waves I: A PDE Approach to Homogenization of Lines of Traffic Lights (Preliminary version)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:01Z",
  "url": "https://research.draconitic.com/paper/3b352phf9ngtq",
  "venue": "HAL",
  "versions": []
}