{
  "id": "1609.01890",
  "version": "v1",
  "published": "2016-09-07T09:03:00.000Z",
  "updated": "2016-09-07T09:03:00.000Z",
  "title": "On recovering parabolic diffusions from their time-averages",
  "authors": [
    "Nikolai Dokuchaev"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The paper study a possibility to recover a parabolic diffusion from its time-average when the values at the initial time are unknown. This problem can be reformulated as a new boundary value problem where a Cauchy condition is replaced by a prescribed time-average of the solution. It is shown that this new problem is well-posed. The paper establishes existence, uniqueness, and a regularity of the solution for this new problem and its modifications, including problems with singled out terminal values.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-07T09:03:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K20",
      "35Q99",
      "32A35"
    ],
    "keywords": [
      "recovering parabolic diffusions",
      "boundary value problem",
      "paper establishes existence",
      "initial time",
      "cauchy condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}