{
  "id": "0806.4915",
  "version": "v1",
  "published": "2008-06-30T15:11:12.000Z",
  "updated": "2008-06-30T15:11:12.000Z",
  "title": "Diffusive stability of oscillations in reaction-diffusion systems",
  "authors": [
    "Thierry Gallay",
    "Arnd Scheel"
  ],
  "comment": "29 pages, no figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study nonlinear stability of spatially homogeneous oscillations in reaction-diffusion systems. Assuming absence of unstable linear modes and linear diffusive behavior for the neutral phase, we prove that spatially localized perturbations decay algebraically with the diffusive rate t^{-n/2} in space dimension n. We also compute the leading order term in the asymptotic expansion of the solution, and show that it corresponds to a spatially localized modulation of the phase. Our approach is based on a normal form transformation in the kinetics ODE which partially decouples the phase equation, at the expense of making the whole system quasilinear. Stability is then obtained by a global fixed point argument in temporally weighted Sobolev spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-06-30T15:11:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K57",
      "35B10",
      "35B35",
      "35B40"
    ],
    "keywords": [
      "reaction-diffusion systems",
      "diffusive stability",
      "oscillations",
      "localized perturbations decay",
      "global fixed point argument"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.4915G"
    }
  }
}