{
  "id": "1302.4265",
  "version": "v2",
  "published": "2013-02-18T13:34:33.000Z",
  "updated": "2013-04-18T13:07:53.000Z",
  "title": "Hyperbolic Relaxation of Reaction Diffusion Equations with Dynamic Boundary Conditions",
  "authors": [
    "Ciprian G. Gal",
    "Joseph L. Shomberg"
  ],
  "comment": "to appear in Quarterly of Applied Mathematics",
  "categories": [
    "math.DS",
    "math.AP"
  ],
  "abstract": "Under consideration is the hyperbolic relaxation of a semilinear reaction-diffusion equation on a bounded domain, subject to a dynamic boundary condition. We also consider the limit parabolic problem with the same dynamic boundary condition. Each problem is well-posed in a suitable phase space where the global weak solutions generate a Lipschitz continuous semiflow which admits a bounded absorbing set. We prove the existence of a family of global attractors of optimal regularity. After fitting both problems into a common framework, a proof of the upper-semicontinuity of the family of global attractors is given as the relaxation parameter goes to zero. Finally, we also establish the existence of exponential attractors.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-18T13:07:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B41",
      "35B21",
      "35L20",
      "35K57"
    ],
    "keywords": [
      "dynamic boundary condition",
      "reaction diffusion equations",
      "hyperbolic relaxation",
      "global attractors",
      "global weak solutions generate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.4265G"
    }
  }
}