Publications [#287369] of James H. Nolen

Papers Published

1. Nolen, J; Xin, J, Existence of KPP type fronts in space-time periodic shear flows and a study of minimal speeds based on variational principle, Discrete and Continuous Dynamical Systems, vol. 13 no. 5 (January, 2005), pp. 1217-1234, American Institute of Mathematical Sciences (AIMS) [pdf], [doi]
   (last updated on 2024/04/24)

   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.