274 research outputs found
Existence of KPP Type Fronts in Space-Time Periodic Shear Flows and a Study of Minimal Speeds Based on Variational Principle
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
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