Ballistic aggregation in symmetric and nonsymmetric flows

We consider explicit solutions to the problem of ballistic aggregation of dustlike matter whose particles stick together absolutely inelastically upon collisions—a description of the formation of a large-scale structure in cosmology in terms of the adhesion model, which is a generalization of the Zel’dovich approximation. The two previously suggested different representations of the solutions for a plane-symmetric 1D flow are shown to be equivalent. Explicit representations of the solutions in cylindrical and spherical symmetries are constructed. We provide explicit examples showing that the two representations under consideration cannot be generalized to a multidimensional nonsymmetric flow.