{
  "id": "1310.4978",
  "version": "v1",
  "published": "2013-10-18T11:39:49.000Z",
  "updated": "2013-10-18T11:39:49.000Z",
  "title": "Entire Solutions for Bistable Lattice Differential Equations with Obstacles",
  "authors": [
    "A. Hoffman",
    "H. J. Hupkes",
    "E. Van Vleck"
  ],
  "comment": "96 pages",
  "categories": [
    "math.DS",
    "math.AP"
  ],
  "abstract": "We consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions we show that wave-like solutions exist when obstacles (characterized by \"holes\") are present in the lattice. Our work generalizes to the discrete spatial setting the results obtained in a paper of Berestycki, Hamel and Matano for the propagation of waves around obstacles in continuous spatial domains. The analysis hinges upon the development of sub and super-solutions for a class of discrete bistable reaction-diffusion problems and on a generalization of a classical result due to Aronson and Weinberger that concerns the spreading of localized disturbances.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-18T11:39:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34K31",
      "37L15"
    ],
    "keywords": [
      "bistable lattice differential equations",
      "entire solutions",
      "scalar lattice differential equations",
      "discrete bistable reaction-diffusion problems",
      "square lattices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 96,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.4978H"
    }
  }
}