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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Abstract

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

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

Dates
First available in Project Euclid: 13 April 2006

Permanent link to this document
https://projecteuclid.org/euclid.maa/1144939950

Mathematical Reviews number (MathSciNet)
MR2195373

Zentralblatt MATH identifier
1107.35366

Subjects
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

Citation

Nolen, James; Xin, Jack. Min-max variational principle and front speeds in random shear flows. Methods Appl. Anal. 11 (2004), no. 4, 635--644. https://projecteuclid.org/euclid.maa/1144939950


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