{
  "id": "1811.02223",
  "version": "v1",
  "published": "2018-11-06T08:47:43.000Z",
  "updated": "2018-11-06T08:47:43.000Z",
  "title": "Decay properties and asymptotic profiles for elastic waves with Kelvin-Voigt damping in 2D",
  "authors": [
    "Wenhui Chen"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we consider elastic waves with Kelvin-Voigt damping in 2D. For the linear problem, applying pointwise estimates in the Fourier space and asymptotic expansion of eigenvalues, we establish sharp energy decay estimates with additional $L^m$ regularity and $L^p-L^q$ estimates on the conjugate line. Furthermore, we derive asymptotic profiles of solutions under different assumptions of the initial data. For the semilinear problem, we use the derived $L^2-L^2$ estimates with additional $L^m$ regularity to prove global (in time) existence of small data solutions to the weakly coupled system. Finally, to deal with elastic waves with Kelvin-Vogit damping in 3D, we apply the Helmholtz decomposition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-06T08:47:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L52",
      "35L71",
      "35B40"
    ],
    "keywords": [
      "elastic waves",
      "asymptotic profiles",
      "kelvin-voigt damping",
      "decay properties",
      "establish sharp energy decay estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}