{
  "id": "1611.06994",
  "version": "v1",
  "published": "2016-11-21T20:19:02.000Z",
  "updated": "2016-11-21T20:19:02.000Z",
  "title": "Diffraction of Elastic Waves by Edges",
  "authors": [
    "Vitaly Katsnelson"
  ],
  "comment": "40 pages, 2 figures. arXiv admin note: text overlap with arXiv:math/0612750 by other authors",
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate the diffraction of singularities of solutions to the linear elastic equation on manifolds with edge singularities. Such manifolds are modeled on the product of a smooth manifold and a cone over a compact fiber. For the fundamental solution, the initial pole generates a pressure wave (p-wave), and a secondary, slower shear wave (s wave). If the initial pole is appropriately situated near the edge, we show that when a p-wave strikes the edge, the diffracted p-waves and s-waves (i.e. loosely speaking, do not correspond to limits of p-rays which just miss the edge) are weaker in a Sobolev sense than the incident p-wave. We also show an analogous result for an s-wave that hits the edge, and provide results for more general situations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-21T20:19:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elastic waves",
      "diffraction",
      "initial pole generates",
      "linear elastic equation",
      "slower shear wave"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}