  Propagation of traveling fronts in three-dimensional reaction-diffusion media
with spatially modulated cross-section is studied using the Schl\"ogl model as
a representative example. Applying appropriate perturbation techniques leads
first to a reduction of dimensionality in which the spatially dependent Neumann
boundary condition translate into a boundary-induced advection term and,
secondly, to an equation of motion for the traveling wave position in weakly
corrugated confinements. Comparisons with numerical simulations demonstrate
that our analytical results properly predicts the nonlinear dependence of the
propagation velocity on ratio of the spatial period of the confinement to the
intrinsic width of the front; including the peculiarity of propagation failure.
Based on the eikonal equation, we obtain an analytical estimate for the finite
interval of propagation failure. Lastly, we demonstrate that the front velocity
is determined by the suppressed diffusivity of the reactants if the intrinsic
width of the front is much larger than the spatial variation of the medium.
