Math @ Duke

Publications [#287369] of James H. Nolen
Papers Published
 Nolen, J; Xin, J, Existence of KPP type fronts in spacetime periodic shear flows and a study of minimal speeds based on variational principle,
Discrete and Continuous Dynamical Systems, vol. 13 no. 5
(2005),
pp. 12171234 [pdf]
(last updated on 2017/12/14)
Abstract: We prove the existence of reactiondiffusion traveling fronts in mean zero spacetime periodic shear flows for nonnegative reactions including the classical KPP (KolmogorovPetrovskyPiskunov) nonlinearity. For the KPP nonlinearity, the minimal front speed is characterized by a variational principle involving the principal eigenvalue of a spacetime periodic parabolic operator. Analysis of the variational principle shows that adding a meanzero space time periodic shear flow to an existing mean zero spaceperiodic 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 reactiondiffusion obeys quadratic and linear laws at small and large shear amplitudes.


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