Curved fronts in a shear flow: case of combustion nonlinearities

We prove the existence and uniqueness, up to a shift in time, of curved traveling fronts for a reaction-advection-diffusion equation with a combustion-type nonlinearity. The advection is through a shear flow $q$. This analyzes, for instance, the shape of flames produced by a Bunsen burner in the presence of advection. We also give a formula for the speed of propagation of these conical fronts in terms of the well-known speed of planar pulsating traveling waves.