Abstract
The theory of optimal control of systems described by equations with partial derivatives is rich in results and is actively developing nowadays. The popularity of this kind of research is connected with their active use in solving problems of natural science, in particular, hydro- and gas dynamics, filtration, diffusion, heat physics, theory of biological populations. The problem of choosing the optimal system control described by the boundary value problem for $2b$-parabolic equations with an integral non-local condition and limited internal, boundary and starting control is investigated. The quality criterion is given by the sum of volume and surface integrals. Using Green's function of the general boundary value problem for the $2b$ parabolic equation, the existence, uniqueness, and integral image of the solutions of the nonlocal boundary value problem for the $2b$ parabolic equation with the integral condition on the time variable have been established. Estimates of the solution of the nonlocal boundary value problem and its derivatives in H\"{o}lder spaces are found. The obtained results are used to establish the necessary and sufficient conditions for the existence of an optimal solution of systems described by a parabolic boundary value problem with a nonlocal integral condition for the time variable. The cases of limited internal, starting and boundary controls are considered.
Published Version
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