{
  "id": "0904.3615",
  "version": "v1",
  "published": "2009-04-23T08:13:01.000Z",
  "updated": "2009-04-23T08:13:01.000Z",
  "title": "Lipschitz metric for the Hunter-Saxton equation",
  "authors": [
    "Alberto Bressan",
    "Helge Holden",
    "Xavier Raynaud"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study stability of solutions of the Cauchy problem for the Hunter-Saxton equation $u_t+uu_x=\\frac14(\\int_{-\\infty}^xu_x^2 dx-\\int_{x}^\\infty u_x^2 dx)$ with initial data $u_0$. In particular, we derive a new Lipschitz metric $d_\\D$ with the property that for two solutions $u$ and $v$ of the equation we have $d_\\D(u(t),v(t))\\le e^{Ct} d_\\D(u_0,v_0)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-23T08:13:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q53",
      "35B35",
      "35Q20"
    ],
    "keywords": [
      "hunter-saxton equation",
      "lipschitz metric",
      "study stability",
      "cauchy problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.3615B"
    }
  }
}