{
  "id": "1509.05598",
  "version": "v1",
  "published": "2015-09-18T12:00:37.000Z",
  "updated": "2015-09-18T12:00:37.000Z",
  "title": "Asymptotic for a second order evolution equation with convex potential and vanishing damping term",
  "authors": [
    "Ramzi May"
  ],
  "comment": "5 pages",
  "categories": [
    "math.OC"
  ],
  "abstract": "In this short note, we recover by a different method the new result due to Attouch, Peyrouqet and Redont concerning the weak convergence as $t\\rightarrow+\\infty$ of solutions $x(t)$ to the second order differential equation \\[ x^{\\prime\\prime}(t)+\\frac{K}{t}x^{\\prime}(t)+\\nabla\\Phi(x(t))=0, \\] where $K>3$ and $\\Phi$ is a smooth convex function defined on an Hilbert Space $\\mathcal{H}.$ Moreover, we improve slightly their result on the rate of convergence of $\\Phi(x(t))-\\min\\Phi.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-18T12:00:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "second order evolution equation",
      "vanishing damping term",
      "convex potential",
      "second order differential equation",
      "asymptotic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150905598M"
    }
  }
}