{
  "id": "1508.03206",
  "version": "v1",
  "published": "2015-08-13T13:26:23.000Z",
  "updated": "2015-08-13T13:26:23.000Z",
  "title": "A reinterpretation of set differential equations as differential equations in a Banach space",
  "authors": [
    "Martin Rasmussen",
    "Janosch Rieger",
    "Kevin Webster"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Set differential equations are usually formulated in terms of the Hukuhara differential, which implies heavy restrictions for the nature of a solution. We propose to reformulate set differential equations as ordinary differential equations in a Banach space by identifying the convex and compact subsets of $\\R^d$ with their support functions. Using this representation, we demonstrate how existence and uniqueness results can be applied to set differential equations. We provide a simple example, which can be treated in support function representation, but not in the Hukuhara setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-13T13:26:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58D25",
      "34G20",
      "26E25"
    ],
    "keywords": [
      "banach space",
      "reformulate set differential equations",
      "reinterpretation",
      "ordinary differential equations",
      "support function representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150803206R"
    }
  }
}