  In this study, we investigate a porous medium-type flux limited
reaction--diffusion equation that arises in morphogenesis modeling. This
nonlinear partial differential equation is an extension of the generalized
Fisher--Kolmogorov--Petrovsky--Piskunov (Fisher-KPP) equation in
one-dimensional space. The approximate analytical traveling wave solution is
found by using a perturbation method. We show that the morphogen concentration
propagates as a sharp wave front where the wave speed has a saturated value.
The numerical solutions of this equation are also provided to compare them with
the analytical predictions. Finally, we qualitatively compare our theoretical
results with those obtained in experimental studies.
