Methods and Applications of Analysis

KPP Front Speeds in Random Shears and the Parabolic Anderson Problem

Jack Xin

Abstract

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.

Article information

Source
Methods Appl. Anal., Volume 10, Number 2 (2003), 191-198.

Dates
First available in Project Euclid: 17 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.maa/1119018752

Mathematical Reviews number (MathSciNet)
MR2074747

Zentralblatt MATH identifier
1052.35099

Citation

Xin, Jack. KPP Front Speeds in Random Shears and the Parabolic Anderson Problem. Methods Appl. Anal. 10 (2003), no. 2, 191--198. https://projecteuclid.org/euclid.maa/1119018752


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