{
  "id": "1210.7853",
  "version": "v2",
  "published": "2012-10-29T22:25:02.000Z",
  "updated": "2015-02-02T22:41:17.000Z",
  "title": "Short-time stability of scalar viscous shocks in the inviscid limit by the relative entropy method",
  "authors": [
    "Kyudong Choi",
    "Alexis F. Vasseur"
  ],
  "comment": "Changed its title to emphasize an inviscid limit. Minor revision on the introduction. No result has been changed",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider inviscid limits to shocks for viscous scalar conservation laws in one space dimension, with strict convex fluxes. We show that we can obtain sharp estimates in $L^2$, for a class of large perturbations and for any bounded time interval. Those perturbations can be chosen big enough to destroy the viscous layer. This shows that the fast convergence to the shock does not depend on the fine structure of the viscous layers. This is the first application of the relative entropy method developed in [22], [23] to the study of an inviscid limit to a shock.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-29T22:25:02.000Z",
      "title": "Relative entropy applied to the stability of viscous shocks up to a translation for scalar conservation laws",
      "abstract": "We consider inviscid limits to shocks for viscous scalar conservation laws in one space dimension, with strict convex fluxes. We show that we can obtain sharp estimates in $L^2$, for a class of large perturbations. Those perturbations can be chosen big enough to destroy the viscous layer. This shows that the fast convergence to the shock does not depend on the fine structure of the viscous layers. This is the first application of the relative entropy method developed in [22], [23] to the study of an asymptotic limit to a shock.",
      "comment": "17 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-02T22:41:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35L65",
      "35L67"
    ],
    "keywords": [
      "relative entropy",
      "viscous shocks",
      "translation",
      "strict convex fluxes",
      "viscous scalar conservation laws"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.7853C"
    }
  }
}