  We develop a semi-analytic model of hierarchical galaxy formation with an
improved treatment of the evolution of galaxies inside dark matter haloes. We
take into account not only dynamical friction processes building up the central
dominant galaxy, but also binary aggregations of satellite galaxies inside a
common halo described using the kinetic Smoluchowski equation. The description
of gas cooling, star formation and evolution, and Supernova feedback follows
the standard prescriptions widely used in semi-analytic modelling. We find that
binary aggregations are effective in depleting the number of small/intermediate
mass galaxies over the redshift range 1<z<3, thus flattening the slope of the
luminosity function at the faint end. At z~0 the flattening occurs for
-20<M_B<-18, but an upturn is obtained at the very faint end for M_B>-16. We
compare our predicted luminosity functions with those obtained from deep
multicolor surveys in the rest-frame B and UV bands for the redshift ranges
0<z<1 and 2.5<z<3.5, respectively. The comparison shows that the discrepancy of
the predictions of other semi-analytic models with the observations is
considerably reduced at z>1 and even more at z ~ 3 by the effect of binary
aggregations. The predictions from our dynamical model are discussed and
compared with the effects of complementary processes which may conspire in
affecting the shape of the luminosity function.
