{
  "id": "1407.5712",
  "version": "v2",
  "published": "2014-07-22T02:21:30.000Z",
  "updated": "2014-07-29T19:29:13.000Z",
  "title": "Lagrangian Variational Framework for Boundary Value Problems",
  "authors": [
    "Alexander Figotin",
    "Guillermo Reyes"
  ],
  "comment": "41 pages, 3 figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "A boundary value problem is commonly associated with constraints imposed on a system at its boundary. We advance here an alternative point of view treating the system as interacting \"boundary\" and \"interior\" subsystems. This view is implemented through a Lagrangian framework that allows to account for (i) a variety of forces including dissipative acting at the boundary; (ii) a multitude of features of interactions between the boundary and the interior fields when the boundary fields may differ from the boundary limit of the interior fields; (iii) detailed pictures of the energy distribution and its flow; (iv) linear and nonlinear effects. We provide a number of elucidating examples of the structured boundary and its interactions with the system interior. We also show that the proposed approach covers the well known boundary value problems.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-29T19:29:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49S05"
    ],
    "keywords": [
      "boundary value problem",
      "lagrangian variational framework",
      "interior fields",
      "interactions",
      "lagrangian framework"
    ],
    "publication": {
      "doi": "10.1063/1.4931135",
      "journal": "Journal of Mathematical Physics",
      "year": 2015,
      "month": "Sep",
      "volume": 56,
      "number": 9,
      "pages": "093506"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JMP....56i3506F"
    }
  }
}