{
  "id": "1503.07703",
  "version": "v1",
  "published": "2015-03-26T12:27:26.000Z",
  "updated": "2015-03-26T12:27:26.000Z",
  "title": "A probabilistic approach to large time behaviour of parabolic equations with Neumann boundary conditions",
  "authors": [
    "Ying Hu",
    "Pierre-Yves Madec"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper is devoted to the study of the large time behaviour of viscosity solutions of parabolic equations with Neumann boundary conditions. This work is the sequel of [12] in which a probabilistic method was developped to show that the solution of a parabolic semilinear PDE behaves like a linear term $\\lambda$T shifted with a function v, where (v, $\\lambda$) is the solution of the ergodic PDE associated to the parabolic PDE. We adapt this method in finite dimension by a penalization method in order to be able to apply an important basic coupling estimate result and with the help of a regularization procedure in order to avoid the lack of regularity of the coefficients in finite dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-26T12:27:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "neumann boundary conditions",
      "large time behaviour",
      "parabolic equations",
      "probabilistic approach",
      "parabolic semilinear pde behaves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150307703H"
    }
  }
}