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September 2004 Variational Principle Based Computation of KPP Average Front Speeds in Random Shear Flows
James Nolen, Jack Xin
Methods Appl. Anal. 11(3): 389-398 (September 2004).


Variational principle of Kolmogorov-Petrovsky-Piskunov (KPP) minimal front speeds provides a fast and accurate way for speed calculations. A variational principle based computation is carried out on a large ensemble of KPP random speeds through spatial, mean zero, stationary, Gaussian random shear flows inside two dimensional channel domains. In the regime of small root mean square (rms) shear amplitude, the enhancement of the ensemble averaged KPP front speed obeys the quadratic law. In the large rms amplitude regime, the enhancement follows the linear law. An asymptotic ensemble averaged speed formula is derived and agrees well with the numerics. Related theoretical results are presented with a brief outline of the ideas in the proofs. The ensemble averaged speed is found to increase sublinearly with enlarging channel widths, while the speed variance decreases. Direct simulations in the small rms regime suggest quadratic speed enhancement law for non-KPP nonlinearities.


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James Nolen. Jack Xin. "Variational Principle Based Computation of KPP Average Front Speeds in Random Shear Flows." Methods Appl. Anal. 11 (3) 389 - 398, September 2004.


Published: September 2004
First available in Project Euclid: 11 May 2006

zbMATH: 1128.76050
MathSciNet: MR2214682

Rights: Copyright © 2004 International Press of Boston

Vol.11 • No. 3 • September 2004
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