BIFURCATIONS OF TRAVELING 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 framew ork of large activation energies. The physical situation is well estab lished, due to the classical work of Sivashinsky. He derived a dispers ion 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 theo ry, furthering a study of D. Terman. We then investigate the bifurcati on in detail. Finally, we investigate the three-dimensional case, wher e a different bifurcation pattern may occur.