  This paper is concerned with the analysis of speed-up of
reaction-diffusion-advection traveling fronts in infinite cylinders with
periodic boundary conditions. The advection is a shear flow with a large
amplitude and the reaction is nonnegative, with either positive or zero
ignition temperature. The unique or minimal speeds of the traveling fronts are
proved to be asymptotically linear in the flow amplitude as the latter goes to
infinity, solving an open problem from \cite{b}. The asymptotic growth rate is
characterized explicitly as the unique or minimal speed of traveling fronts for
a limiting degenerate problem, and the convergence of the regular traveling
fronts to the degenerate ones is proved for positive ignition temperatures
under an additional H{\"{o}}rmander-type condition on the flow.
