{
  "id": "1204.4397",
  "version": "v1",
  "published": "2012-04-19T16:09:15.000Z",
  "updated": "2012-04-19T16:09:15.000Z",
  "title": "Smooth solutions for a ${p}$-system of mixed type",
  "authors": [
    "Michael",
    "Bialy"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "In this note we analyze smooth solutions of a $p$-system of the \\textit{mixed} type. Motivating example for this is a 2-components reduction of the Benney moments chain which appears to be connected to theory of integrable systems. We don't assume a-priory that the solutions in question are in the Hyperbolic region. Our main result states that the only smooth solutions of the system which are periodic in $x$ are necessarily constants. As for initial value problem we prove that if the initial data is strictly hyperbolic and periodic in $x$ then the solution can not extend to $[t_0;+\\infty)$ and shocks are necessarily created.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-19T16:09:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L65",
      "35L67",
      "70H06"
    ],
    "keywords": [
      "mixed type",
      "initial value problem",
      "benney moments chain",
      "main result states",
      "dont assume a-priory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.4397M"
    }
  }
}