{
  "id": "1902.03279",
  "version": "v1",
  "published": "2019-02-08T20:22:44.000Z",
  "updated": "2019-02-08T20:22:44.000Z",
  "title": "Unique Continuation Properties for solutions to the Camassa-Holm equation and other non-local equations",
  "authors": [
    "Felipe Linares",
    "Gustavo Ponce"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "It is shown that if $\\,u(x,t)\\,$ is a solution of the initial value problem for the Camassa-Holm equation which vanishes in an open set $\\,\\Omega\\subset \\mathbb R\\times [0,T]$, then $\\,u(x,t)=0,\\,(x,t)\\in\\mathbb R\\times [0,T]$. This result also applies to solutions of the initial periodic boundary value problems associated to the Camassa-Holm equation. The argument of proof can be placed in a general setting to extend the above results to a class of non-linear non-local 1-dimensional models which includes the Degasperis-Procesi equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-08T20:22:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q51",
      "37K10"
    ],
    "keywords": [
      "camassa-holm equation",
      "unique continuation properties",
      "non-local equations",
      "initial periodic boundary value problems",
      "initial value problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}