{
  "id": "1503.08807",
  "version": "v1",
  "published": "2015-03-30T19:30:25.000Z",
  "updated": "2015-03-30T19:30:25.000Z",
  "title": "Structurally Stable Singularities for a Nonlinear Wave Equation",
  "authors": [
    "Alberto Bressan",
    "Tao Huang",
    "Fang Yu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "For the nonlinear wave equation $u_{tt} - c(u)\\big(c(u) u_x\\big)_x~=~0$, it is well known that solutions can develop singularities in finite time. For an open dense set of initial data, the present paper provides a detailed asymptotic description of the solution in a neighborhood of each singular point, where $|u_x|\\to\\infty$. The different structure of conservative and dissipative solutions is analyzed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-30T19:30:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear wave equation",
      "structurally stable singularities",
      "open dense set",
      "initial data",
      "detailed asymptotic description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}