{
  "id": "0908.2226",
  "version": "v1",
  "published": "2009-08-16T09:48:37.000Z",
  "updated": "2009-08-16T09:48:37.000Z",
  "title": "Improved intermediate asymptotics for the heat equation",
  "authors": [
    "Jean-Philippe Bartier",
    "Adrien Blanchet",
    "Jean Dolbeault",
    "Miguel Escobedo"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This letter is devoted to results on intermediate asymptotics for the heat equation. We study the convergence towards a stationary solution in self-similar variables. By assuming the equality of some moments of the initial data and of the stationary solution, we get improved convergence rates using entropy / entropy-production methods. We establish the equivalence of the exponential decay of the entropies with new, improved functional inequalities in restricted classes of functions. This letter is the counterpart in a linear framework of a recent work on fast diffusion equations, see [Bonforte-Dolbeault-Grillo-Vazquez]. Results extend to the case of a Fokker-Planck equation with a general confining potential.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-16T09:48:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D10",
      "35K10",
      "35K15",
      "47J20"
    ],
    "keywords": [
      "heat equation",
      "intermediate asymptotics",
      "stationary solution",
      "fast diffusion equations",
      "general confining potential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.2226B"
    }
  }
}