{
  "id": "1205.3578",
  "version": "v2",
  "published": "2012-05-16T07:14:52.000Z",
  "updated": "2013-04-15T11:05:08.000Z",
  "title": "A degenerating PDE system for phase transitions and damage",
  "authors": [
    "Elisabetta Rocca",
    "Riccarda Rossi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we analyze a PDE system arising in the modeling of phase transition and damage phenomena in thermoviscoelastic materials. The resulting evolution equations in the unknowns \\theta (absolute temperature), u (displacement), and \\chi (phase/damage parameter) are strongly nonlinearly coupled. Moreover, the momentum equation for u contains \\chi-dependent elliptic operators, which degenerate at the pure phases (corresponding to the values \\chi=0 and \\chi=1), making the whole system degenerate. That is why, we have to resort to a suitable weak solvability notion for the analysis of the problem: it consists of the weak formulations of the heat and momentum equation, and, for the phase/damage parameter \\chi, of a generalization of the principle of virtual powers, partially mutuated from the theory of rate-independent damage processes. To prove an existence result for this weak formulation, an approximating problem is introduced, where the elliptic degeneracy of the displacement equation is ruled out: in the framework of damage models, this corresponds to allowing for partial damage only. For such an approximate system, global-in-time existence and well-posedness results are established in various cases. Then, the passage to the limit to the degenerate system is performed via suitable variational techniques.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-15T11:05:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "degenerating pde system",
      "phase transition",
      "phase/damage parameter",
      "momentum equation",
      "weak formulation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.3578R"
    }
  }
}