{
  "id": "1508.07232",
  "version": "v1",
  "published": "2015-08-26T22:28:42.000Z",
  "updated": "2015-08-26T22:28:42.000Z",
  "title": "On a problem of S.L. Sobolev",
  "authors": [
    "Michael V. Klibanov"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In 1930 Sergey L. Sobolev [7,8] has proposed a construction of the solution of the Cauchy problem for the hyperbolic equation of the second order with variable coefficients in 3-d. Although Sobolev did not construct the fundamental solution, his construction was modified later by Romanov [4,5] to obtain the fundamental solution. However, these works impose a restrictive assumption of the regularity of geodesic lines in a large domain. In addition, it is unclear how to realize those methods numerically. In this paper a simple construction of a function, which is associated in a clear way with the fundamental solution of the acoustic equation with the variable speed in 3-d, is proposed. Conditions on geodesic lines are not imposed. An important feature of this construction is that it lends itself to effective computations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-26T22:28:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fundamental solution",
      "geodesic lines",
      "clear way",
      "hyperbolic equation",
      "simple construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150807232K"
    }
  }
}