{
  "id": "1109.2762",
  "version": "v2",
  "published": "2011-09-13T12:45:37.000Z",
  "updated": "2012-01-12T19:37:04.000Z",
  "title": "On the Large Time Behavior of Solutions of Hamilton-Jacobi Equations Associated with Nonlinear Boundary Conditions",
  "authors": [
    "Guy Barles",
    "Hiroyoshi Mitake",
    "Hitoshi Ishii"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article, we study the large time behavior of solutions of first-order Hamilton-Jacobi Equations, set in a bounded domain with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish general convergence results for viscosity solutions of these Cauchy-Neumann problems by using two fairly different methods : the first one relies only on partial differential equations methods, which provides results even when the Hamiltonians are not convex, and the second one is an optimal control/dynamical system approach, named the \"weak KAM approach\" which requires the convexity of Hamiltonians and gives formulas for asymptotic solutions based on Aubry-Mather sets.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-12T19:37:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large time behavior",
      "nonlinear boundary conditions",
      "hamilton-jacobi equations",
      "partial differential equations methods",
      "nonlinear neumann boundary conditions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00205-011-0484-1",
      "journal": "Archive for Rational Mechanics and Analysis",
      "year": 2012,
      "month": "May",
      "volume": 204,
      "number": 2,
      "pages": 515
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012ArRMA.204..515B"
    }
  }
}