{
  "id": "1109.0452",
  "version": "v2",
  "published": "2011-09-02T14:16:13.000Z",
  "updated": "2012-02-28T08:12:14.000Z",
  "title": "Estimates for a class of oscillatory integrals and decay rates for wave-type equations",
  "authors": [
    "Anton Arnold",
    "JinMyong Kim",
    "Xiaohua Yao"
  ],
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "This paper investigates higher order wave-type equations of the form $\\partial_{tt}u+P(D_{x})u=0$, where the symbol $P(\\xi)$ is a real, non-degenerate elliptic polynomial of the order $m\\ge4$ on ${\\bf R}^n$. Using methods from harmonic analysis, we first establish global pointwise time-space estimates for a class of oscillatory integrals that appear as the fundamental solutions to the Cauchy problem of such wave equations. These estimates are then used to establish (pointwise-in-time) $L^p-L^q$ estimates on the wave solution in terms of the initial conditions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-02-28T08:12:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B37",
      "35L25",
      "35B65"
    ],
    "keywords": [
      "oscillatory integrals",
      "decay rates",
      "higher order wave-type equations",
      "first establish global pointwise time-space",
      "establish global pointwise time-space estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.0452A"
    }
  }
}