The problem of choosing an optimal control for a system described by a boundary value problem for 2b-parabolic equations with an integral nonlocal condition and limited internal, boundary, and starting control is investigated. The quality criterion is given by the sum of volume and surface integrals. Using the Green function of the general boundary value problem for a 2b-parabolic equation, the existence, uniqueness, and integral representation of solutions of a nonlocal boundary value problem for a 2b-parabolic equation with an integral condition over a time variable are established. Estimates of the solution of the nonlocal boundary value problem and its derivatives in Hölder spaces are found. The obtained results are used to establish necessary and sufficient conditions for the existence of an optimal solution for systems described by a parabolic boundary value problem with a nonlocal integral condition over a time variable. The cases of bounded internal, starting, and boundary controls are considered.

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