A Variational Principle Based Study of KPP Minimal Front Speeds in Random Shears
arXiv:math/0410564 · doi:10.1088/0951-7715/18/4/013
Abstract
Variational principle for Kolmogorov-Petrovsky-Piskunov (KPP) minimal front speeds provides an efficient tool for statistical speed analysis, as well as a fast and accurate method for speed computation. A variational principle based analysis is carried out on the ensemble of KPP speeds through spatially stationary random shear flows inside infinite channel domains. In the regime of small root mean square (rms) shear amplitude, the enhancement of the ensemble averaged KPP front speeds is proved to obey the quadratic law under certain shear moment conditions. Similarly, in the large rms amplitude regime, the enhancement follows the linear law. In particular, both laws hold for the Ornstein-Uhlenbeck process in case of two dimensional channels. An asymptotic ensemble averaged speed formula is derived in the small rms regime and is explicit in case of the Ornstein-Uhlenbeck process of the shear. Variational principle based computation agrees with these analytical findings, and allows further study on the speed enhancement distributions as well as the dependence of enhancement on the shear covariance. Direct simulations in the small rms regime suggest quadratic speed enhancement law for non-KPP nonlinearities.
28 pages, 14 figures update: fixed typos, refined estimates in section 2
References in corpus (3)
Cited by in corpus (5)
- Thin front propagation in random shear flows
- Existence, Stability and Bifurcation of Random Complete and Periodic Solutions of Stochastic Parabolic Equations
- Diffusive KPP Equations with Free Boundaries in Time Almost Periodic Environments: I. Spreading and Vanishing Dichotomy
- Diffusive KPP Equations with Free Boundaries in Time Almost Periodic Environments: II. Spreading Speeds and Semi-Wave
- Variational Principle of KPP Front Speeds in Temporally Random Shear Flows