{
  "id": "1810.00458",
  "version": "v1",
  "published": "2018-09-30T20:32:11.000Z",
  "updated": "2018-09-30T20:32:11.000Z",
  "title": "Geometry and Conservation Laws for a Class of Second-Order Parabolic Equations I: Geometry",
  "authors": [
    "Benjamin B. McMillan"
  ],
  "comment": "34 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "I consider the geometry of the class of scalar parabolic equations using Cartan's method of equivalence. After defining the exterior differential systems that correspond to general second order parabolic equations in arbitrarily many variables, I define local invariants of parabolic equations up to contact transformation. The first family of invariants determine when a parabolic system has a deprolongation to a parabolic Monge-Amp\\`ere system. The second family of invariants determine when a general parabolic equation has a local choice of coordinates putting it in evolutionary form. In addition to intrinsic interest, another motivation is to study the conservation laws of parabolic equations. The invariants developed in this paper are crucial to the results on conservation laws in Part II of this 2 part series of papers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-30T20:32:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "58A15",
      "35K96"
    ],
    "keywords": [
      "conservation laws",
      "second-order parabolic equations",
      "general second order parabolic equations",
      "invariants determine",
      "general parabolic equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}