{
  "id": "2406.09102",
  "version": "v1",
  "published": "2024-06-13T13:29:45.000Z",
  "updated": "2024-06-13T13:29:45.000Z",
  "title": "Analytic smoothing effect of the Cauchy problem for a class of ultra-parabolic equations",
  "authors": [
    "Xiao-Dong Cao",
    "Chao-Jiang Xu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study a class of strongly degenerate ultraparabolic equations with analytic coefficients. We demonstrate that the Cauchy problem exhibits an analytic smoothing effect. This means that, with an initial datum belonging to the Sobolev space $H^s$ (of real index s), the associated Cauchy problem admits a unique solution that is analytic in all spatial variables for any strictly positive time. This smoothing effect property is similar to that of the Cauchy problem for uniformly parabolic equations with analytic coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-13T13:29:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "analytic smoothing effect",
      "ultra-parabolic equations",
      "analytic coefficients",
      "associated cauchy problem admits",
      "strongly degenerate ultraparabolic equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}