{
  "id": "1310.3779",
  "version": "v1",
  "published": "2013-10-14T18:45:56.000Z",
  "updated": "2013-10-14T18:45:56.000Z",
  "title": "Invariant measure of scalar first-order conservation laws with stochastic forcing",
  "authors": [
    "Arnaud Debussche",
    "Julien Vovelle"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Under an hypothesis of non-degeneracy of the flux, we study the long-time behaviour of periodic scalar first-order conservation laws with stochastic forcing in any space dimension. For sub-cubic fluxes, we show the existence of an invariant measure. Moreover for sub-quadratic fluxes we show uniqueness and ergodicity of the invariant measure. Also, since this invariant measure is supported by Lp for some p small, we are led to generalize to the stochastic case the theory of L1 solutions developed by Chen and Perthame in 2003.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-14T18:45:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "invariant measure",
      "stochastic forcing",
      "periodic scalar first-order conservation laws",
      "long-time behaviour",
      "space dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.3779D"
    }
  }
}