The Singularities of Type of Shock Waves in Pressureless Medium, the Solutions in the Sense of Measures and Kolombo's Sense

The preprint studies the system of equations consisting of the 2-D Burgers equation and continuity equation. Such system was proposed by Ya.Zel'dovich in 1970 to describe the formation of the large-scale structure of the Universe. In the paper for the divergent form of this system (appears to be the gas dynamics system without pressure) the rigorous notion of generalized solutions in terms of Radon measures is formulated and the generalization of Rankin-Hugoniot conditions is obtained. On the basis of such conditions it is shown that the variational representation for the generalized solutions, which is valid for 1-D case, for 2-D case in general does not take place. In the framework of more general theory of Kolombo's generalized functions the Rankin-Hugoniot conditions keep the same form.