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.

No abstract

No abstract

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.

We obtain conditions to find the distributed optimal control for parabolic-hyperbolic equations with nonlocal boundary conditions and general quadratic criterion in the special norm. The unique solvability of systems for finding the optimal solution is established, systems' kernels are estimated, and the convergence of solutions of the problem is proved.