{
  "id": "2204.01179",
  "version": "v1",
  "published": "2022-04-03T23:06:49.000Z",
  "updated": "2022-04-03T23:06:49.000Z",
  "title": "Local existence and uniqueness of a quasilinear system of equations as the fixed point of a Fibonacci-contraction",
  "authors": [
    "Felipe Angeles"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The Cauchy problem for a quasilinear system of hyperbolic-parabolic equations is addressed with the method of linearization and fixed point. Coupling between the hyperbolic and parabolic variables is allowed and we do not assume the Friedrich's symmetrizability of the system. This coupling results in weaker linear energy estimates and Banach's fixed point theorem cannot be applied. A metric fixed point theorem is developed in order to conclude the local existence and uniqueness of solutions. We apply our results to the Cattaneo-Christov system for viscous compressible fluid flow, a system of equations whose inviscid part is not hyperbolic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-03T23:06:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local existence",
      "quasilinear system",
      "uniqueness",
      "weaker linear energy estimates",
      "fibonacci-contraction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}