{
  "id": "1411.4153",
  "version": "v1",
  "published": "2014-11-15T14:51:58.000Z",
  "updated": "2014-11-15T14:51:58.000Z",
  "title": "Petviashvilli's Method for the Dirichlet Problem",
  "authors": [
    "Derek Olson",
    "Soumitra Shukla",
    "Gideon Simpson",
    "Daniel Spirn"
  ],
  "comment": "33 pages, 10 figures",
  "categories": [
    "math.AP",
    "math.NA"
  ],
  "abstract": "We examine the Petviashvilli method for solving the equation $ \\phi - \\Delta \\phi = |\\phi|^{p-1} \\phi$ on a bounded domain $\\Omega \\subset \\mathbb{R}^d$ with Dirichlet boundary conditions. We prove that a ground state is a local attractor of the iteration procedure, similar to the results on $\\mathbb{R}^d$ by Pelinovsky and Stepanyants (2004). We prove a global convergence result by generating a suite of nonlinear inequalities for the iteration sequence, and we show that the sequence has a natural energy that decreases along the sequence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-15T14:51:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35C08",
      "65N12"
    ],
    "keywords": [
      "petviashvillis method",
      "dirichlet problem",
      "dirichlet boundary conditions",
      "global convergence result",
      "iteration sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.4153O"
    }
  }
}