{
  "id": "2001.07780",
  "version": "v1",
  "published": "2020-01-21T21:28:56.000Z",
  "updated": "2020-01-21T21:28:56.000Z",
  "title": "Concentration and homogenization in electrical conduction in heterogeneous media involving the Laplace-Beltrami operator",
  "authors": [
    "Micol Amar",
    "Daniele Andreucci",
    "Roberto Gianni",
    "Claudia Timofte"
  ],
  "comment": "36 pages, 3 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a concentration and homogenization problem modelling electrical conduction in a composite material. The novelty of the problem is due to the specific scaling of the physical quantities characterizing the dielectric component of the composite. This leads to the appearance of a peculiar displacement current governed by a Laplace-Beltrami pseudo-parabolic equation. This pseudo-parabolic character is present also in the homogenized equation, which is obtained by the unfolding technique.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-21T21:28:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B27",
      "35K70",
      "74Q10"
    ],
    "keywords": [
      "laplace-beltrami operator",
      "heterogeneous media",
      "concentration",
      "homogenization problem modelling electrical conduction",
      "peculiar displacement current"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}