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June 2003 KPP Front Speeds in Random Shears and the Parabolic Anderson Problem
Jack Xin
Methods Appl. Anal. 10(2): 191-198 (June 2003).


We study the asymptotics of front speeds of the reaction-diffusion equations with Kolmogorov-Petrovsky-Piskunov (KPP) nonlinearity and zero mean stationary ergodic Gaussian shear advection on the entire plane. By exploiting connections of KPP front speeds with the almost sure Lyapunov exponents of the parabolic Anderson problem, and with the homogenized Hamiltonians of Hamilton-Jacobi equations, we show that front speeds enhancement is quadratic in the small root mean square (rms) amplitudes of white in time zero mean Gaussian shears, and it grows at the order of the large rms amplitudes. However, front speeds diverge logarithmically if the shears are time independent zero mean stationary ergodic Gaussian fields.


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Jack Xin. "KPP Front Speeds in Random Shears and the Parabolic Anderson Problem." Methods Appl. Anal. 10 (2) 191 - 198, June 2003.


Published: June 2003
First available in Project Euclid: 17 June 2005

zbMATH: 1052.35099
MathSciNet: MR2074747

Rights: Copyright © 2003 International Press of Boston


Vol.10 • No. 2 • June 2003
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