{
  "id": "1408.6146",
  "version": "v1",
  "published": "2014-08-26T15:13:21.000Z",
  "updated": "2014-08-26T15:13:21.000Z",
  "title": "Optimal boundary control of a viscous Cahn-Hilliard system with dynamic boundary condition and double obstacle potentials",
  "authors": [
    "Pierluigi Colli",
    "M. Hassan Farshbaf-Shaker",
    "Gianni Gilardi",
    "Jürgen Sprekels"
  ],
  "comment": "Key words: optimal control; parabolic obstacle problems; MPECs; dynamic boundary conditions; optimality conditions. arXiv admin note: substantial text overlap with arXiv:1308.5617",
  "categories": [
    "math.AP",
    "math.OC"
  ],
  "abstract": "In this paper, we investigate optimal boundary control problems for Cahn-Hilliard variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace-Beltrami operator. The cost functional is of standard tracking type, and box constraints for the controls are prescribed. We prove existence of optimal controls and derive first-order necessary conditions of optimality. The general strategy, which follows the lines of the recent approach by Colli, Farshbaf-Shaker, Sprekels (see Appl. Math. Optim., 2014) to the (simpler) Allen-Cahn case, is the following: we use the results that were recently established by Colli, Gilardi, Sprekels in the preprint arXiv:1407.3916 [math.AP] for the case of (differentiable) logarithmic potentials and perform a so-called \"deep quench limit\". Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired first-order necessary optimality conditions for the case of (non-differentiable) double obstacle potentials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-26T15:13:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "74M15",
      "49K20",
      "35K61"
    ],
    "keywords": [
      "double obstacle potentials",
      "dynamic boundary condition",
      "viscous cahn-hilliard system",
      "first-order necessary optimality conditions",
      "optimal boundary control problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.6146C"
    }
  }
}