Bifurcations of travelling waves in the thermo-diffusive model for flame propagation

The main topic of this paper is the study of steady-state bifurcations occurring in the two-dimensional thermo-diffusive model in the framework of large activation energies.The physical situation is well established, due to the classical work of Sivashinsky. He derived a dispersion relation and observed that the planar waves bifurcated into stable multidimensional waves as the Lewis number crossed a critical value.The purpose of this paper is to give a mathematical basis to this theory, furthering a study of D. Terman. We then investigate the bifurcation in detail. Finally, we investigate the three-dimensional case, where a different bifurcation pattern may occur.