{
  "id": "2009.07319",
  "version": "v1",
  "published": "2020-09-15T18:47:13.000Z",
  "updated": "2020-09-15T18:47:13.000Z",
  "title": "Asymptotics of Fundamental Solution of Cauchy Problem for Parabolic Equation with Small Parameter and Degeneration",
  "authors": [
    "Mark Rakhel"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, the method of constructing the asymptotics of the fundamental solution of the Cauchy problem for a degenerate linear parabolic equation with small diffusion is considered. Based on the results obtained in \\cite{dn}, the study extends them over the case of a degenerate equation. As in \\cite{dn}, the main technique that allows us to switch from pseudo-differential equations to partial differential equations is the non-oscillating WKB method. A distinctive feature of this work is a more detailed consideration on the characteristics of the Green's function in terms of symplectic geometry. The most significant intermediate result is presented as a theorem on the properties of the fundamental solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-15T18:47:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fundamental solution",
      "cauchy problem",
      "small parameter",
      "asymptotics",
      "degenerate linear parabolic equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}