Degenerate flows of solving operators for nonstationary Sobolev type equations

Research of stationary Sobolev type equations were the basis for the study of a variety of different problems, such as optimal control problem, Leontief type system, the optimal measurement problems, etc. Nonstationary Sobolev type equations have been studied only in fragments. In this article the methods required to find solutions to such equations are substantiated. Namely, we investigate degenerate flows of solving operators with which shows the solvability of initial value problems for nonstationary equations of Sobolev type.