{
  "id": "math/0407366",
  "version": "v1",
  "published": "2004-07-21T22:16:25.000Z",
  "updated": "2004-07-21T22:16:25.000Z",
  "title": "Existence of KPP Type Fronts in Space-Time Periodic Shear Flows and a Study of Minimal Speeds Based on Variational Principle",
  "authors": [
    "James Nolen",
    "Jack Xin"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove the existence of reaction-diffusion traveling fronts in mean zero space-time periodic shear flows for nonnegative reactions including the classical KPP (Kolmogorov-Petrovsky-Piskunov) nonlinearity. For the KPP nonlinearity, the minimal front speed is characterized by a variational principle involving the principal eigenvalue of a space-time periodic parabolic operator. Analysis of the variational principle shows that adding a mean-zero space time periodic shear flow to an existing mean zero space-periodic shear flow leads to speed enhancement. Computation of KPP minimal speeds is performed based on the variational principle and a spectrally accurate discretization of the principal eigenvalue problem. It shows that the enhancement is monotone decreasing in temporal shear frequency, and that the total enhancement from pure reaction-diffusion obeys quadratic and linear laws at small and large shear amplitudes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-07-21T22:16:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "space-time periodic shear flows",
      "variational principle",
      "kpp type fronts",
      "minimal speeds",
      "zero space-periodic shear flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......7366N"
    }
  }
}