Mass and momentum distribution of galaxies producing during merging and the problem of activity of nuclei

The exactly soluble problem of merging under the condition of conservation of mass and momentum in a statistically homogeneous galaxy system is considered. Comparatively simple analytic expressions are obtained for the asymptotics pertaining to large masses, momenta and times. The solutions correspond to constancy of the merging coefficient. In the case when the coefficient depends on the mass, it is possible to design a self-similar combination of variables which describes the propagation of a stationary front toward large masses. The asymptotics of the initial distribution, with allowance for cosmological expansion, is also considered. The possible relation between mass and momentum distributions and the activity of the galaxies is discussed briefly