{
  "id": "1607.02224",
  "version": "v1",
  "published": "2016-07-08T05:29:52.000Z",
  "updated": "2016-07-08T05:29:52.000Z",
  "title": "A perturbation problem involving singular perturbations of domains for Hamilton-Jacobi equations",
  "authors": [
    "Taiga Kumagai"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate a singular perturbation for Hamilton-Jacobi equations in an open subset of two dimensional Euclidean space, where the set is determined through a Hamiltonian function and the Hamilton-Jacobi equations are the dynamic programming equations for optimal control of the Hamiltonian flow of the Hamiltonian. We establish the convergence of solutions of the Hamilton-Jacobi equations and identify the limit of the solutions as solutions of systems of ordinary differential equations on a graph. The perturbation is singular in the sense that the domain degenerates to the graph in the limit process. Our result can be seen as a perturbation analysis, in the viewpoint of optimal control, of the Hamiltonian flow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-08T05:29:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hamilton-jacobi equations",
      "singular perturbation",
      "perturbation problem",
      "hamiltonian flow",
      "optimal control"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}