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{1144939950,
author = {Nolen, James and Xin, Jack},
title = {Min-max variational principle and front speeds in random shear flows},
journal = {Methods Appl. Anal.},
volume = {11},
number = {1},
year = {2004},
pages = { 635-644},
language = {en},
url = {http://dml.mathdoc.fr/item/1144939950}
}
Nolen, James; Xin, Jack. Min-max variational principle and front speeds in random shear flows. Methods Appl. Anal., Tome 11 (2004) no. 1, pp. 635-644. http://gdmltest.u-ga.fr/item/1144939950/