{
  "id": "math/0607456",
  "version": "v2",
  "published": "2006-07-19T09:34:18.000Z",
  "updated": "2006-08-16T11:31:21.000Z",
  "title": "Well-posedness of the Cauchy problem for the fractional power dissipative equations",
  "authors": [
    "Changxing Miao",
    "Baoquan Yuan",
    "Bo Zhang"
  ],
  "comment": "30pages",
  "journal": "Nonlinear Analysis 68(2008)461-484",
  "doi": "10.1016/j.na.2006.11.011",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper studies the Cauchy problem for the nonlinear fractional power dissipative equation $u_t+(-\\triangle)^\\alpha u= F(u)$ for initial data in the Lebesgue space $L^r(\\mr^n)$ with $\\ds r\\ge r_d\\triangleq{nb}/({2\\alpha-d})$ or the homogeneous Besov space $\\ds\\dot{B}^{-\\sigma}_{p,\\infty}(\\mr^n)$ with $\\ds\\sigma=(2\\alpha-d)/b-n/p$ and $1\\le p\\le \\infty$, where $\\alpha>0$, $F(u)=f(u)$ or $Q(D)f(u)$ with $Q(D)$ being a homogeneous pseudo-differential operator of order $d\\in[0,2\\alpha)$ and $f(u)$ is a function of $u$ which behaves like $|u|^bu$ with $b>0$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-08-16T11:31:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K05",
      "35K15"
    ],
    "keywords": [
      "cauchy problem",
      "well-posedness",
      "nonlinear fractional power dissipative equation",
      "homogeneous pseudo-differential operator",
      "paper studies"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7456M"
    }
  }
}