{
  "id": "1808.07743",
  "version": "v1",
  "published": "2018-08-23T13:31:24.000Z",
  "updated": "2018-08-23T13:31:24.000Z",
  "title": "Weighted ultrafast diffusion equations: from well-posedness to long-time behaviour",
  "authors": [
    "Mikaela Iacobelli",
    "Francesco Patacchini",
    "Filippo Santambrogio"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we devote our attention to a class of weighted ultrafast diffusion equations arising from the problem of quantisation for probability measures. These equations have a natural gradient flow structure in the space of probability measures endowed with the quadratic Wasserstein distance. Exploiting this structure, in particular through the so-called JKO scheme, we introduce a notion of weak solutions, prove existence, uniqueness, BV and H^1 estimates, L^1 weighted contractivity, Harnack inequalities, and exponential convergence to a steady state.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-23T13:31:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "long-time behaviour",
      "natural gradient flow structure",
      "probability measures",
      "well-posedness",
      "quadratic wasserstein distance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}