{
  "id": "0903.4679",
  "version": "v1",
  "published": "2009-03-26T19:43:21.000Z",
  "updated": "2009-03-26T19:43:21.000Z",
  "title": "Large time behavior of solutions of viscous Hamilton-Jacobi Equations with superquadratic Hamiltonian",
  "authors": [
    "Thierry Wilfried Tabet Tchamba"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the long-time behavior of the unique viscosity solution $u$ of the viscous Hamilton-Jacobi Equation $u_t-\\Delta u + |Du|^m = f\\hbox{in }\\Omega\\times (0,+\\infty)$ with inhomogeneous Dirichlet boundary conditions, where $\\Omega$ is a bounded domain of $\\mathbb{R}^N$. We mainly focus on the superquadratic case ($m>2$) and consider the Dirichlet conditions in the generalized viscosity sense. Under rather natural assumptions on $f,$ the initial and boundary data, we connect the problem studied to its associated stationary generalized Dirichlet problem on one hand and to a stationary problem with a state constraint boundary condition on the other hand.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-26T19:43:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "viscous hamilton-jacobi equation",
      "large time behavior",
      "superquadratic hamiltonian",
      "stationary generalized dirichlet problem",
      "state constraint boundary condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.4679W"
    }
  }
}