{
  "id": "1208.1032",
  "version": "v1",
  "published": "2012-08-05T16:07:00.000Z",
  "updated": "2012-08-05T16:07:00.000Z",
  "title": "On the Approximate Controllability of Stackelberg-Nash Strategies for Linear Heat Equations in $\\mathbb{R}^N$ with Potentials",
  "authors": [
    "Isaías P. de Jesus",
    "Silvano B. de Menezes"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper we establish hierarchic control for the linear heat equation in $\\re^N$ with potentials. Our strategy is inspired by the techniques developed by J.I. D\\'iaz and J.-L. Lions \\cite{DL}; however many new difficulties arise due to lack of compactness of Sobolev embeddings. We manage these adversities by employing similarity variables and weighted Sobolev spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-05T16:07:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear heat equation",
      "stackelberg-nash strategies",
      "approximate controllability",
      "potentials",
      "establish hierarchic control"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.1032D"
    }
  }
}