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December 2004 Min-max variational principle and front speeds in random shear flows
James Nolen, Jack Xin
Methods Appl. Anal. 11(4): 635-644 (December 2004).


Speed ensemble of bistable (combustion) fronts in mean zero stationary Gaussian shear flows inside two and three dimensional channels is studied with a min-max variational principle. In the small root mean square regime of shear flows, a new class of multi-scale test functions are found to yield speed asymptotics. The quadratic speed enhancement law holds with probability arbitrarily close to one under the almost sure continuity (dimension two) and mean square Hölder regularity (dimension three) of the shear flows. Remarks are made on the quadratic and linear laws of front speed expectation in the small and large root mean square regimes.


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James Nolen. Jack Xin. "Min-max variational principle and front speeds in random shear flows." Methods Appl. Anal. 11 (4) 635 - 644, December 2004.


Published: December 2004
First available in Project Euclid: 13 April 2006

zbMATH: 1107.35366
MathSciNet: MR2195373

Primary: 76F10
Secondary: 35K57 , 35R60 , 41A60 , 65Mxx , 76M30 , 76M35

Rights: Copyright © 2004 International Press of Boston

Vol.11 • No. 4 • December 2004
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