Propagation of a Pulsating Flame Front in a Gaseous Combustible Mixture

We employ a diffusional-thermal model derived by Matkowsky and Sivashinsky for chemically reacting gases, to show the existence of a pulsating flame front in a premixed combustible gas governed by a one-step Arrhenius reaction. We show that the pulsating front arises as a time-periodic bifurcation from a uniformly propagating plane flame front when the Lewis number L exceeds a critical value Lc. For L > Lc, the plane front becomes unstable and perturbations of the system evolve to the pulsating state