Strongly nonlinear asymptotic model of cellular instabilities in   premixed flames with stepwise ignition temperature kinetics
  In this paper we consider ignition-temperature, first-order reaction model of thermo-diffusive combustion that describes dynamics of thick flames arising in a theory of combustion of hydrogen-oxygen and ethylene-oxygen mixtures. These flames often assume the shape of propagating curved interfaces that correspond to level sets of constant temperature. We derive a fully nonlinear equation that governs dynamics of these level sets under a single assumption of small curvature. We study this equation for various asymptotic parameter regimes and discuss the ranges of validity of the corresponding simplified models. Our theoretical findings are supported by numerical simulations. 
Nathan Kilker, Dmitry Golovaty, Peter V. Gordon, Leonid Kagan, Gregory   I. Sivashinsky
nlin.CD