Methods and Applications of Analysis

Min-max variational principle and front speeds in random shear flows

James Nolen and Jack Xin

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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.

Article information

Methods Appl. Anal., Volume 11, Number 4 (2004), 635-644.

First available in Project Euclid: 13 April 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 76F10: Shear flows
Secondary: 35K57: Reaction-diffusion equations 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15] 65Mxx: Partial differential equations, initial value and time-dependent initial- boundary value problems 76M30: Variational methods 76M35: Stochastic analysis


Nolen, James; Xin, Jack. Min-max variational principle and front speeds in random shear flows. Methods Appl. Anal. 11 (2004), no. 4, 635--644.

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