{
  "id": "math/0006094",
  "version": "v1",
  "published": "2000-06-13T15:12:33.000Z",
  "updated": "2000-06-13T15:12:33.000Z",
  "title": "Stability of $L^\\infty$ solutions for hyperbolic systems with coinciding shocks and rarefactions",
  "authors": [
    "Stefano Bianchini"
  ],
  "comment": "19 pages, 13 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a hyperbolic system of conservation laws u_t + f(u)_x = 0 and u(0,\\cdot) = u_0, where each characteristic field is either linearly degenerate or genuinely nonlinear. Under the assumption of coinciding shock and rarefaction curves and the existence of a set of Riemann coordinates $w$, we prove that there exists a semigroup of solutions $u(t) = \\mathcal{S}_t u_0$, defined on initial data $u_0 \\in L^\\infty$. The semigroup $\\mathcal{S}$ is continuous w.r.t. time and the initial data $u_0$ in the $L^1_{\\text{loc}}$ topology. Moreover $\\mathcal{S}$ is unique and its trajectories are obtained as limits of wave front tracking approximations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-06-13T15:12:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L65"
    ],
    "keywords": [
      "hyperbolic system",
      "coinciding shock",
      "initial data",
      "wave front tracking approximations",
      "conservation laws"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......6094B"
    }
  }
}