The nonlinear inhomogeneous diffusion equation and the distribution of matter in the early universe

Abstract

New exact solutions of the nonlinear inhomogeneous diffusion equation and the distribution of matter in the early universe calculated using an approximation of the nonlinear stage of expansion by the nonlinear inhomogeneous diffusion equation are found. Matter in the universe is distributed in certain regions. Matter is concentrated on the borders of the regions, its concentration along the border ribs being higher than inside a region and highest in the knots of the regions. In the course of time all matter tends to concentrate in the knots, and inside the regions matter density decreases as b25/2(ln b)23/2.