{
  "id": "1312.1072",
  "version": "v2",
  "published": "2013-12-04T09:18:15.000Z",
  "updated": "2014-03-15T05:23:35.000Z",
  "title": "A Dynamical Approach to Viscosity Solutions of Hamilton-Jacobi Equations",
  "authors": [
    "Lin Wang",
    "Jun Yan"
  ],
  "comment": "This paper has been withdrawn by the author due to a crucial error in Lemma 3.4",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we consider the following Hamilton-Jacobi equation with initial condition: \\begin{equation*} \\begin{cases} \\partial_tu(x,t)+H(x,t,u(x,t),\\partial_xu(x,t))=0, u(x,0)=\\phi(x). \\end{cases} \\end{equation*} Under some assumptions on the convexity of $H(x,t,u,p)$ w.r.t. $p$, we develop a dynamical approach to viscosity solutions and show that there exists an intrinsic connection between viscosity solutions and certain minimal characteristics.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-15T05:23:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "viscosity solutions",
      "hamilton-jacobi equation",
      "dynamical approach",
      "initial condition",
      "intrinsic connection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.1072W"
    }
  }
}