Optimal Control in Higher-Order Sobolev-Type Mathematical Models with $(A,p)$-Bounded Operators

This article deals with the optimal control problem for an incomplete Sobolev-type equation of high order. We prove an existence and uniqueness theorem for strong solutions to the initial value problem for a given equation. We obtain sufficient and necessary conditions for the existence and uniqueness of optimal control of these solutions. We use the ideas and methods developed by G. A. Sviridyuk and his school. The proof of the existence and uniqueness of optimal control rests on the theory of optimal control developed by J.-L. Lions.