{
  "id": "0706.2104",
  "version": "v1",
  "published": "2007-06-14T12:22:08.000Z",
  "updated": "2007-06-14T12:22:08.000Z",
  "title": "Homogenization of nonlinear scalar conservation laws",
  "authors": [
    "Anne-Laure Dalibard"
  ],
  "comment": "34 pages",
  "journal": "Archive for Rational Mechanics and Analysis (2008) ISSN: 0003-9527 (Print) 1432-0673 (Online)",
  "doi": "10.1007/s00205-008-0123-7",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the limit as $\\e\\to 0$ of the entropy solutions of the equation $\\p_t \\ue + \\dv_x[A(\\frac{x}{\\e},\\ue)] =0$. We prove that the sequence $\\ue$ two-scale converges towards a function $u(t,x,y)$, and $u$ is the unique solution of a limit evolution problem. The remarkable point is that the limit problem is not a scalar conservation law, but rather a kinetic equation in which the macroscopic and microscopic variables are mixed. We also prove a strong convergence result in $L^1_{\\text{loc}}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-14T12:22:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B27",
      "35L60"
    ],
    "keywords": [
      "nonlinear scalar conservation laws",
      "homogenization",
      "strong convergence result",
      "limit evolution problem",
      "microscopic variables"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Archive for Rational Mechanics and Analysis",
      "year": 2009,
      "month": "Apr",
      "volume": 192,
      "number": 1,
      "pages": 117
    },
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009ArRMA.192..117D"
    }
  }
}