{
  "id": "1307.1572",
  "version": "v1",
  "published": "2013-07-05T10:18:08.000Z",
  "updated": "2013-07-05T10:18:08.000Z",
  "title": "Existence of solutions for a mathematical model related to solid-solid phase transitions in shape memory alloys",
  "authors": [
    "Elena Bonetti",
    "Pierluigi Colli",
    "Mauro Fabrizio",
    "Gianni Gilardi"
  ],
  "comment": "Key words: nonstandard phase field system, nonlinear partial differential equations, initial-boundary value problem, existence of solutions",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a strongly nonlinear PDE system describing solid-solid phase transitions in shape memory alloys. The system accounts for the evolution of an order parameter (related to different symmetries of the crystal lattice in the phase configurations), of the stress (and the displacement), and of the absolute temperature. The resulting equations present several technical difficulties to be tackled: in particular, we emphasize the presence of nonlinear coupling terms, higher order dissipative contributions, possibly multivalued operators. As for the evolution of temperature, a highly nonlinear parabolic equation has to be solved for a right hand side that is controlled only in L^1. We prove the existence of a solution for a regularized version, by use of a time discretization technique. Then, we perform suitable a priori estimates which allow us pass to the limit and find a weak global-in-time solution to the system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-05T10:18:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A01",
      "35M33",
      "35Q79",
      "74C10"
    ],
    "keywords": [
      "shape memory alloys",
      "mathematical model",
      "describing solid-solid phase transitions",
      "system describing solid-solid phase",
      "pde system describing solid-solid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.1572B"
    }
  }
}