{
  "id": "1309.2385",
  "version": "v1",
  "published": "2013-09-10T06:35:05.000Z",
  "updated": "2013-09-10T06:35:05.000Z",
  "title": "Thresholds for global existence and blow-up in a general class of doubly dispersive nonlocal wave equations",
  "authors": [
    "Saadet Erbay",
    "Husnu A. Erbay",
    "Albert Erkip"
  ],
  "comment": "17 pages. Accepted for publication in Nonlinear Analysis:Theory, Methods & Applications",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article we study global existence and blow-up of solutions for a general class of nonlocal nonlinear wave equations with power-type nonlinearities, $u_{tt}-Lu_{xx}=B(- |u|^{p-1}u)_{xx}, ~(p>1)$, where the nonlocality enters through two pseudo-differential operators $L$ and $B$. We establish thresholds for global existence versus blow-up using the potential well method which relies essentially on the ideas suggested by Payne and Sattinger. Our results improve the global existence and blow-up results given in the literature for the present class of nonlocal nonlinear wave equations and cover those given for many well-known nonlinear dispersive wave equations such as the so-called double-dispersion equation and the traditional Boussinesq-type equations, as special cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-10T06:35:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "doubly dispersive nonlocal wave equations",
      "global existence",
      "general class",
      "nonlocal nonlinear wave equations",
      "nonlinear dispersive wave equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.2385E"
    }
  }
}