{
  "id": "1811.03705",
  "version": "v1",
  "published": "2018-11-08T22:53:49.000Z",
  "updated": "2018-11-08T22:53:49.000Z",
  "title": "Ultracontractivity and Gaussian bounds for evolution families associated with non-autonomous forms",
  "authors": [
    "Hafida Laasri",
    "Delio Mugnolo"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We develop a variational approach in order to study qualitative properties of non-autonomous parabolic equations. Based on the method of product integrals, we discuss invariance properties and ultracontractivity of evolution families in Hilbert space. Our main results give sufficient conditions for the heat kernel of the evolution family to satisfy Gaussian-type bounds. Along the way, we study examples of non-autonomous equations on graphs, metric graphs, and domains.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-08T22:53:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47D06",
      "47D07",
      "47A07",
      "35K90"
    ],
    "keywords": [
      "evolution family",
      "gaussian bounds",
      "non-autonomous forms",
      "ultracontractivity",
      "satisfy gaussian-type bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}