Special Session 19: Stochastic Partial Differential Equations

Brownian fluctuations of flame fronts with small random advection

Christopher Henderson
University of Arizona
Co-Author(s):    Panagiotis Souganidis
We discuss the effect of small random advection in two models of front propagation in turbulent combustion. We (i) identify the order of the fluctuations of the front with respect to the size of the advection, and (ii) characterize them by the solution of a Hamilton-Jacobi equation forced by white noise. In the simplest case, the result yields, for both models, a front with Brownian fluctuations of the same scale as the size of the advection. That the fluctuations are the same for both models is somewhat surprising, in view of known differences between the two models in the large advection regime. We also mention connections to weakly inhomogeneous ASEP.