{
  "id": "1810.02161",
  "version": "v1",
  "published": "2018-10-04T11:58:00.000Z",
  "updated": "2018-10-04T11:58:00.000Z",
  "title": "Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics",
  "authors": [
    "Georgy Kitavtsev",
    "Roman M. Taranets"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we extend the results of [1] by proving exponential asymptotic $H^1$-convergence of solutions to a one-dimensional singular heat equation with $L^2$-source term that describe evolution of viscous thin liquid sheets while considered in the Lagrange coordinates. Furthermore, we extend this asymptotic convergence result to the case of a time inhomogeneous source. This study has also independent interest for the porous medium equation theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-04T11:58:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35G31",
      "76D27",
      "76D45",
      "35K59"
    ],
    "keywords": [
      "long-time behaviour",
      "application",
      "hydrodynamics",
      "one-dimensional singular heat equation",
      "porous medium equation theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}