We prove that the problem of optimal control for the Poisson equation with nonlocal boundary conditions in a circular sector has a classical solution in the class of distributed controls.

We consider the linear-quadratic optimal control problem for parabolic equation with nonlocal boundary conditions in a circular sector with quadratic cost functional. Using the biorthonormal basis systems of functions and Fourier-Bessel series, we prove the classical solvability of such problem in special classes of distributed controls and initial functions. IntroductionAmong a variety of classical and modern methods for analysis of infinite-dimensional optimal control problems [1-4], Fourier method remains a powerful tool to solve linear-quadratic problems for distributed systems. In many cases, this method allows to decompose initial problem and reduce it to countable number of one-dimensional optimal control problems.In this paper, we consider a minimization problem for quadratic cost functional on the solutions of linear parabolic equation with nonlocal boundary conditions in a circular sector. A classical solvability of such boundary value problem for Laplace equation was proved in the paper [5], using biorthonormal basis systems of functions.

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