We investigate the propagation and interaction of a rupture front that propagates on a planar fault using a boundary integral equation method. We show first that the rupture velocity is controlled by a delicate balance between consumed fracture energy and supplied elastic strain energy. A very sharp boundary in parameter space separates models in which ruptures stop spontaneously from those in which rupture propagates at super-shear speeds. The transition zone (or bifurcation) is shown to be stable with reference to small-scale heterogeneities of the stress field. Using the relations derived from this analysis we examined the mechanism to generate high slip rate when two rupture fronts collide. We found that collision at slow rupture velocities causes abrupt stress drop and generates high slip rates. However, these features tend to be moderated by large slip-weakening distances. Finally, we simulated rupture front focusing at the initial stages of an earthquake, a phenomenon that may cause high slip rate pulses and therefore generate high frequency seismic waves. We assume a pre-slip region, in which stress has decreased quasi-statically to the dynamic friction level. Due to this pre-slip, strong stress concentration has developed around the pre-slip area and a dynamic rupture starts at a certain point on the rim of the pre-slip region. We observe rupture front focusing that generates high slip rate pulses. We also studied a double pre-slip model, in which two pre-slip regions exist close to each other before the earthquake and found that multiple pre-slips enhance the focusing effects.