G-equations are well-known front propagation models in turbulent combustion which describe the front motion law in the form of local normal velocity equal to a constant (laminar speed) plus the normal projection of fluid velocity. In level set formulation, G-equations are HamiltonJacobi equations with convex (<i>L</i> ¹ type) but non-coercive Hamiltonians. Viscous G-equations arise from either numerical approximations or regularizations by small diffusion. The nonlinear eigenvalue $${\bar H}$$ from the cell problem of the viscous G-equation can be viewed as an approximation of the inviscid turbulent flame speed <i>s</i> _T. An important problem in turbulent combustion theory is to study properties of <i>s</i> _T, in particular how <i>s</i> _T depends on the flow amplitude <i>A</i>. In this paper, we study the behavior of $${\bar H=\bar H(A,d)}$$ as <i>A</i> + at any fixed diffusion constant <i>d</i> &gt; 0. For cellular flow, we show that$$\bar H(A,d)\leqq

We study the large-time asymptotic shock-front speed in an inviscid Burgers equation with a spatially random flux function. This equation is a prototype for a class of scalar conservation laws with spatial random coefficients such as the well-known BuckleyLeverett equation for two-phase flows, and the contaminant transport equation in groundwater flows. The initial condition is a shock located at the origin (the indicator function of the negative real line). We first regularize the equation by a special random viscous term so that the resulting equation can be solved explicitly by a ColeHopf formula. Using the invariance principle of the underlying random processes and the Laplace method, we prove that for large times the solutions behave like fronts moving at averaged constant speeds in the sense of distribution. However, the front locations are random, and we show explicitly the probability of observing the

The shape stability of the reaction interface for reactive flow in a layered porous medium is studied. This is done using a complete linearized stability analysis in the setting of a free boundary model of this phenomenon. The spectrum of the linearized problem is obtained in the general case, and it is compared with that obtained for homogeneous media in two typical cases.

We study an efficient dynamic blind source separation algorithm of convolutive sound mixtures based on updating statistical information in the frequency domain, and minimizing the support of time domain demixing filters by a weighted least square method. The permutation and scaling indeterminacies of separation, and concatenations of signals in adjacent time frames are resolved with optimization of l 1 l norm on cross-correlation coefficients at multiple time lags. The algorithm is a direct method without iterations, and is adaptive to the environment. Computations on recorded benchmark mixtures of speech and music signals show excellent performance. The method in general separates a foreground source from a background of sounds as often encountered in realistic situations.

METHODS AND APPLICATIONS OF ANALYSIS. c 2009 International Press Vol. 16, No. 4, pp. 507520, December 2009 006