{
  "id": "2206.08334",
  "version": "v1",
  "published": "2022-06-16T17:38:16.000Z",
  "updated": "2022-06-16T17:38:16.000Z",
  "title": "On quasilinear parabolic systems and FBSDEs of quadratic growth",
  "authors": [
    "Joe Jackson"
  ],
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "Using probabilistic methods, we establish a-priori estimates for two classes of quasilinear parabolic systems of partial differential equations (PDEs). We treat in particular the case of a nonlinearity which has quadratic growth in the gradient of the unknown. As a result of our estimates, we obtain the existence of classical solutions of the PDE system. From this, we infer the existence of solutions to a corresponding class of forward-backward stochastic differential equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-16T17:38:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H30"
    ],
    "keywords": [
      "quasilinear parabolic systems",
      "quadratic growth",
      "forward-backward stochastic differential equations",
      "partial differential equations",
      "establish a-priori estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}