{
  "id": "0912.1797",
  "version": "v2",
  "published": "2009-12-09T16:49:00.000Z",
  "updated": "2010-12-15T14:41:05.000Z",
  "title": "On a Model for Mass Aggregation with Maximal Size",
  "authors": [
    "Ondrej Budáč",
    "Michael Herrmann",
    "Barbara Niethammer",
    "Andrej Spielmann"
  ],
  "comment": "new version with revised proofs; 13 pages, several figures",
  "journal": "Kinetic and Related Models, vol. 4, no. 2, pp. 427-439, 2012",
  "doi": "10.3934/krm.2011.4.427",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study a kinetic mean-field equation for a system of particles with different sizes, in which particles are allowed to coagulate only if their sizes sum up to a prescribed time-dependent value. We prove well-posedness of this model, study the existence of self-similar solutions, and analyze the large-time behavior mostly by numerical simulations. Depending on the parameter $\\Dconst$, which controls the probability of coagulation, we observe two different scenarios: For $\\Dconst>2$ there exist two self-similar solutions to the mean field equation, of which one is unstable. In numerical simulations we observe that for all initial data the rescaled solutions converge to the stable self-similar solution. For $\\Dconst<2$, however, no self-similar behavior occurs as the solutions converge in the original variables to a limit that depends strongly on the initial data. We prove rigorously a corresponding statement for $\\Dconst\\in (0,1/3)$. Simulations for the cross-over case $\\Dconst=2$ are not completely conclusive, but indicate that, depending on the initial data, part of the mass evolves in a self-similar fashion whereas another part of the mass remains in the small particles.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-12-15T14:41:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "45K05",
      "82C22"
    ],
    "keywords": [
      "mass aggregation",
      "initial data",
      "maximal size",
      "self-similar solution",
      "solutions converge"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.1797B"
    }
  }
}