{
  "id": "0906.2206",
  "version": "v2",
  "published": "2009-06-11T20:30:37.000Z",
  "updated": "2016-09-04T10:50:28.000Z",
  "title": "Renormalization Group Analysis of Nonlinear Diffusion Equations with Periodic Coefficients",
  "authors": [
    "Gastao A. Braga",
    "Frederico Furtado",
    "Jussara M. Moreira",
    "Leonardo T. Rolla"
  ],
  "journal": "SIAM Multiscale Modeling and Simulation, v. 1, n. 4, p. 630-644, 2003",
  "categories": [
    "math.AP",
    "math.NA"
  ],
  "abstract": "In this paper we present an efficient numerical approach based on the Renormalization Group method for the computation of self-similar dynamics. The latter arise, for instance, as the long-time asymptotic behavior of solutions to nonlinear parabolic partial differential equations. We illustrate the approach with the verification of a conjecture about the long-time behavior of solutions to a certain class of nonlinear diffusion equations with periodic coefficients. This conjecture is based on a mixed argument involving ideas from homogenization theory and the Renormalization Group method. Our numerical approach provides a detailed picture of the asymptotics, including the determination of the effective or renormalized diffusion coefficient.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-11T20:30:37.000Z",
      "comment": "19 pages, including 13 figures. Typeset with LaTeX",
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-09-04T10:50:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35B40",
      "35B33",
      "35B27",
      "74S20"
    ],
    "keywords": [
      "nonlinear diffusion equations",
      "renormalization group analysis",
      "periodic coefficients",
      "renormalization group method",
      "nonlinear parabolic partial differential equations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.2206B"
    }
  }
}