{
  "id": "1411.7265",
  "version": "v1",
  "published": "2014-11-26T15:09:41.000Z",
  "updated": "2014-11-26T15:09:41.000Z",
  "title": "Optimal Control of the Inhomogeneous Relativistic Maxwell Newton Lorentz Equations",
  "authors": [
    "C. Meyer",
    "S. M. Schnepp",
    "O. Thoma"
  ],
  "comment": "32 pages, 8 figures",
  "categories": [
    "math.OC",
    "physics.acc-ph",
    "physics.comp-ph"
  ],
  "abstract": "This note is concerned with an optimal control problem governed by the relativistic Maxwell-Newton-Lorentz equations, which describes the motion of charges particles in electro-magnetic fields and consists of a hyperbolic PDE system coupled with a nonlinear ODE. An external magnetic field acts as control variable. Additional control constraints are incorporated by introducing a scalar magnetic potential which leads to an additional state equation in form of a very weak elliptic PDE. Existence and uniqueness for the state equation is shown and the existence of a global optimal control is established. Moreover, first-order necessary optimality conditions in form of Karush-Kuhn-Tucker conditions are derived. A numerical test illustrates the theoretical findings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-26T15:09:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J20",
      "49J15",
      "49K20",
      "49K15",
      "35Q61"
    ],
    "keywords": [
      "relativistic maxwell newton lorentz equations",
      "inhomogeneous relativistic maxwell newton lorentz",
      "optimal control",
      "first-order necessary optimality conditions",
      "state equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1330342,
      "adsabs": "2014arXiv1411.7265M"
    }
  }
}