{
  "id": "2303.03872",
  "version": "v2",
  "published": "2023-03-07T13:17:53.000Z",
  "updated": "2023-06-27T10:55:25.000Z",
  "title": "Large Time Behavior of Solutions to Hamilton-Jacobi Equations on Networks",
  "authors": [
    "Marco Pozza"
  ],
  "comment": "34 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Starting from Namah and Roquejoffre (1999) and Fathi (1998), the large time asymptotic behavior of solutions to Hamilton--Jacobi equations has been extensively investigated by many authors, mostly on smooth compact manifolds and the flat torus. We extend it to the case where the ambient space is a network. For the well posedness of time dependent problems on networks, the equation must be coupled with a \"flux limiter\", that is the choice of appropriate constants on each vertex of the network. We will investigate the effects of it on the asymptotic analysis.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-06-27T10:55:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35R02",
      "49L25",
      "37J51"
    ],
    "keywords": [
      "large time behavior",
      "hamilton-jacobi equations",
      "large time asymptotic behavior",
      "smooth compact manifolds",
      "time dependent problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}