{
  "id": "0803.1462",
  "version": "v2",
  "published": "2008-03-10T17:45:51.000Z",
  "updated": "2009-05-08T14:31:45.000Z",
  "title": "Regularity, asymptotic behavior and partial uniqueness for Smoluchowski's coagulation equation",
  "authors": [
    "Stéphane Mischler",
    "José Alfredo Cañizo"
  ],
  "journal": "Revista Matem\\'atica Iberoamericana, Vol. 27, No. 3, pp. 803-839 (2011)",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider Smoluchowski's equation with a homogeneous kernel of the form $a(x,y) = x^\\alpha y ^\\beta + x^\\beta y^\\alpha$ with $-1 < \\alpha \\leq \\beta < 1$ and $\\lambda := \\alpha + \\beta \\in (-1,1)$. We first show that self-similar solutions of this equation are infinitely differentiable and prove sharp results on the behavior of self-similar profiles at $y = 0$ in the case $\\alpha < 0$. We also give some partial uniqueness results for self-similar profiles: in the case $\\alpha = 0$ we prove that two profiles with the same mass and moment of order $\\lambda$ are necessarily equal, while in the case $\\alpha < 0$ we prove that two profiles with the same moments of order $\\alpha$ and $\\beta$, and which are asymptotic at $y=0$, are equal. Our methods include a new representation of the coagulation operator, and estimates of its regularity using derivatives of fractional order.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-05-08T14:31:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "smoluchowskis coagulation equation",
      "asymptotic behavior",
      "regularity",
      "self-similar profiles",
      "partial uniqueness results"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.1462M"
    }
  }
}