Problem of hard and optimal control of solutions to the initial-final problem for nonstationary Sobolev type equation

The main aim of this work is solving the problem of hard and optimal control of solution to the initial-finial problem for nonstationary Sobolev type equation. We construct a solution to the initial-final problem for the nonstationary equation and show that a unique optimal control of solutions to this problem exists.
Apart from the introduction and bibliography, the article consists of three sections. The first section provides the essentials of the theory of relatively $p$-bounded operators. In the second section we construct a strong solution to the initial-final problem for nonstationary Sobolev-type equations. The third section contains our proof that there exists a unique optimal control of solutions to the initial-final problem.