  Spin transport equations in a non-homogeneous ferromagnet are derived in the
limit where the sd exchange coupling between the electrons in the conduction
band and those in the d band is dominant. It is shown that spin diffusion in
ferromagnets assumes a tensor form. The diagonal terms are renormalized with
respect to that in normal metals and enhances the dissipation in the magnetic
system while the off-diagonal terms renormalize the precessional frequency of
the conduction electrons and enhances the non-adiabatic spin torque. To
demonstrate the new physics in our theory, we show that self-consistent
solutions of the spin diffusion equations and the Landau-Lifshitz equations in
the presence of a current lead to a an increase in the terminal velocity of a
domain wall which becomes strongly dependent on its width. We also provide a
simplified equation that predicts damping due to the conduction electrons.
