{
  "id": "0903.3703",
  "version": "v1",
  "published": "2009-03-22T05:28:49.000Z",
  "updated": "2009-03-22T05:28:49.000Z",
  "title": "Ultra-analytic effect of Cauchy problem for a class of kinetic equations",
  "authors": [
    "Yoshinori Morimoto",
    "Chao-Jiang Xu"
  ],
  "comment": "22 pages, to appear in JDE",
  "journal": "J. Differential Equations 247 (2009) 597-617",
  "categories": [
    "math.AP"
  ],
  "abstract": "The smoothing effect of the Cauchy problem for a class of kinetic equations is studied. We firstly consider the spatially homogeneous non linear Landau equation with Maxwellian molecules and inhomogeneous linear Fokker-Planck equation to show the ultra-analytic effects of the Cauchy problem. Those smoothing effect results are optimal and similar to heat equation. In the second part, we study a model of spatially inhomogeneous linear Landau equation with Maxwellian molecules, and show the analytic effect of the Cauchy problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-22T05:28:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A05",
      "35B65",
      "35D10",
      "35H20"
    ],
    "keywords": [
      "cauchy problem",
      "ultra-analytic effect",
      "kinetic equations",
      "inhomogeneous linear landau equation",
      "maxwellian molecules"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jde.2009.01.028",
      "journal": "Journal of Differential Equations",
      "year": 2009,
      "volume": 247,
      "number": 2,
      "pages": 596
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009JDE...247..596M"
    }
  }
}