{
  "id": "1508.07641",
  "version": "v1",
  "published": "2015-08-30T21:53:03.000Z",
  "updated": "2015-08-30T21:53:03.000Z",
  "title": "Homogenization of nonstationary Schrödinger type equations with periodic coefficients",
  "authors": [
    "Tatiana Suslina"
  ],
  "comment": "78 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In $L_2(\\mathbb{R}^d;{\\mathbb C}^n)$ we consider selfadjoint strongly elliptic second order differential operators ${\\mathcal A}_\\varepsilon$ with periodic coefficients depending on ${\\mathbf x}/\\varepsilon$. We study the behavior of the operator exponential $\\exp(-i {\\mathcal A}_\\varepsilon \\tau)$, $\\tau \\in {\\mathbb R}$, for small $\\varepsilon$. Approximations for this exponential in the $(H^s\\to L_2)$-operator norm with a suitable $s$ are obtained. The results are applied to study the behavior of the solution ${\\mathbf u}_\\varepsilon$ of the Cauchy problem for the Schr\\\"odinger type equation $i \\partial_\\tau {\\mathbf u}_\\varepsilon = {\\mathcal A}_\\varepsilon {\\mathbf u}_\\varepsilon$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-30T21:53:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B27"
    ],
    "keywords": [
      "nonstationary schrödinger type equations",
      "periodic coefficients",
      "strongly elliptic second order",
      "elliptic second order differential operators",
      "homogenization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 78,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}