{
  "id": "1602.02593",
  "version": "v1",
  "published": "2016-02-05T10:14:11.000Z",
  "updated": "2016-02-05T10:14:11.000Z",
  "title": "Blow up property for viscoelastic evolution equations on manifolds with conical degeneration",
  "authors": [
    "Mohsen Alimohammady",
    "Morteza Koozehgar Kalleji"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is concerned with the study of the nonlinear viscoelastic evolution equation with strong damping and source terms, described by \\[u_{tt} - \\Delta_{\\mathbb{B}}u + \\int_{0}^{t}g(t-\\tau)\\Delta_{\\mathbb{B}}u(\\tau)d\\tau + f(x)u_{t}|u_{t}|^{m-2} = h(x)|u|^{p-2}u , \\hspace{1 cm} x\\in int\\mathbb{B}, t > 0,\\] where $\\mathbb{B}$ is a stretched manifold. First, we prove the solutions of problem {1.1} in cone Sobolev space $\\mathcal{H}^{1,\\frac{n}{2}}_{2,0}(\\mathbb{B}),$ admit a blow up in finite time for $p > m$ and positive initial energy. Then, we construct a lower bound for obtained blow up time under appropriate assumptions on data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-05T10:14:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B44"
    ],
    "keywords": [
      "conical degeneration",
      "nonlinear viscoelastic evolution equation",
      "cone sobolev space",
      "finite time",
      "source terms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160202593A"
    }
  }
}