{
  "id": "1601.05992",
  "version": "v1",
  "published": "2016-01-22T13:22:27.000Z",
  "updated": "2016-01-22T13:22:27.000Z",
  "title": "Explicit exponential convergence to equilibrium for nonlinear reaction-diffusion systems with detailed balance condition",
  "authors": [
    "Klemens Fellner",
    "Bao Quoc Tang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The convergence to equilibrium of mass action reaction-diffusion systems arising from networks of chemical reactions is studied. The considered reaction networks are assumed to satisfy the detailed balance condition and have no boundary equilibria. We propose a general approach based on the so-called entropy method, which is able to quantify with explicitly computable rates the decay of an entropy functional in terms of an entropy entropy-dissipation inequality based on the totality of the conservation laws of the system. As a consequence follows convergence to the unique detailed balance equilibrium with explicitly computable convergence rates. The general approach is further detailed for two important example systems: a single reversible reaction involving an arbitrary number of chemical substances and a chain of two reversible reactions arising from enzyme reactions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-22T13:22:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B35",
      "35B40",
      "35K57",
      "35Q92"
    ],
    "keywords": [
      "detailed balance condition",
      "explicit exponential convergence",
      "nonlinear reaction-diffusion systems",
      "equilibrium",
      "action reaction-diffusion systems arising"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160105992F"
    }
  }
}