  Recent results obtained by analyzing diffuse gamma-ray emission detected by
Fermi-LAT show a substantial variation of the CR spectrum as a function of the
distance from the Galactic Center. For energies up to tens of GeV, the CR
proton density in the outer Galaxy appears to be weakly dependent upon the
galactocentric distance while the density in the central region of the Galaxy
was found to exceed the value measured in the outer Galaxy. At the same time,
Fermi-LAT data suggest a gradual spectral softening while moving outward from
the center of the Galaxy to its outskirts. These findings represent a challenge
for standard calculations of CR propagation based on assuming a uniform
diffusion coefficient within the Galactic volume. Here we present a model of
non-linear CR propagation in which transport is due to particle scattering and
advection off self-generated turbulence. We will show that for a realistic
distribution of CR sources following the spatial distribution of supernova
remnants and the space dependence of the magnetic field on galactocentric
distance, both the spatial profile of CR density and the spectral softening can
easily be accounted for.
