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In the present paper, the Bitsadze-Samarski boundary-value problem is considered for a quasi-linear differential equation of first order on the plane and the existence and uniqueness theorem for a generalized solution is proved; the necessary (in the linear case) and sufficient optimality conditions for optimal control problems are found. The optimal control problem is posed, where the behavior of control functions is described by elliptic-type equations with Bitsadze-Samarski nonlocal boundary conditions. The necessary and sufficient optimality conditions are obtained in the form of the Pontryagin maximum principle and the solution existence and uniqueness theorem is proved for the conjugate problem. Nonlocal boundary-value problems and conjugate problems are solved by the algorithm, which reduces nonlocal boundary value problems to a sequence of Dirichlet problems. The numerical method of solution of an optimal control problem by the Mathcad package is presented. [ABSTRACT FROM AUTHOR]

In this paper, we study optimal control problems whose behavior is described by second-order differential equations with nonlocal Bitsadze-Samarski boundary conditions. Necessary conditions of optimality are obtained in terms of the maximum principle; adjoint equations are constructed in the differential and integral form. Necessary and sufficient optimality conditions are obtained for a linear problem, a difference scheme is constructed and examined, and a numerical algorithm is proposed. [ABSTRACT FROM AUTHOR]

The present paper is devoted to optimal control problems whose behavior is described by quasilinear first-order differential equations on the plane with nonlocal Bitsadze-Samarski boundary conditions. A theorem on the existence and uniqueness of a generalized solution in the space $$ {C}_{\mu}\left(\overline{G}\right) $$ is proved for quasilinear differential equations; necessary optimality conditions are obtained in terms of the maximum principle; the Bitsadze-Samarski boundary-value problem is examined for a first-order linear differential equation; the existence of a solution in the space $$ {C}_{\mu}^p\left(\overline{G}\right) $$ is proved, and an a priori estimate is derived. A necessary and sufficient optimality condition is proved for a linear optimal control problem. [ABSTRACT FROM AUTHOR]

A boundary control problem for the viscous Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions for optimality are proved. [ABSTRACT FROM AUTHOR]

Averaging method is applied to the nonlinear and linear (with respect to control) problems of optimal control on the semiaxis with small parameter and rapidly oscillating coefficients. It is shown that the solutions of the exact problem converge to the solutions of the averaged problem. [ABSTRACT FROM AUTHOR]