{
  "id": "1111.4231",
  "version": "v1",
  "published": "2011-11-17T22:15:24.000Z",
  "updated": "2011-11-17T22:15:24.000Z",
  "title": "The energy decay and asymptotics for a class of semilinear wave equations in two space dimensions",
  "authors": [
    "Soichiro Katayama",
    "Daisuke Murotani",
    "Hideaki Sunagawa"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider semilinear wave equations with small initial data in two space dimensions. For a class of wave equations with cubic nonlinearity, we show the global existence of small amplitude solutions, and give an asymptotic description of the solution as $t \\to \\infty$ uniformly in $x \\in {\\mathbb R}^2$. In particular, our result implies the decay of the energy when the nonlinearity is dissipative.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-17T22:15:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L70",
      "34B40"
    ],
    "keywords": [
      "semilinear wave equations",
      "space dimensions",
      "energy decay",
      "small initial data",
      "small amplitude solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.4231K"
    }
  }
}