{
  "id": "2310.14872",
  "version": "v1",
  "published": "2023-10-23T12:43:40.000Z",
  "updated": "2023-10-23T12:43:40.000Z",
  "title": "On the loss of mass for the heat equation in an exterior domain with general boundary conditions",
  "authors": [
    "Joaquín Domínguez-de Tena",
    "Aníbal Rodríguez-Bernal"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this work, we study the decay of mass for solutions to the heat equation in exterior domains, i.e., domains which are the complement of a compact set in $\\mathbb{R}^N$. Different homogeneous boundary conditions are considered, including Dirichlet, Robin, and Neumann conditions. We determine the exact amount of mass loss and identify criteria for complete mass decay, in which the dimension of the space plays a key role. Furthermore, the paper provides explicit mass decay rates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-23T12:43:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B30",
      "25B40",
      "35E15",
      "35K05"
    ],
    "keywords": [
      "general boundary conditions",
      "exterior domain",
      "heat equation",
      "explicit mass decay rates",
      "complete mass decay"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}