Pyshnograiev I. Optimal control and minmax estimation for parabolic-hyperbolic equations with point nonlocal boundary value conditions

For a fixed control inhomogeneous boundary value problem was solved by separation of variables by a biorthogonal system. The conditions for classical solvability was found. Optimal control problem with semi defined criterion is reduced to a sequence of one-dimensional problems by separation of variables by a Riesz basis. The conditions of optimality and formal control were obtained by direct variation of variables A problem with a distributed and divided control and general quadratic criterion is reduced to a sequence of finite-dimensional problems by separation of variables by Riesz basis. The necessary and sufficient conditions for optimality were shown. It is proven the convergence of the approximate solution of the sequence control to optimal control problems. For distributed and shared observations minimax estimation problem is reduced to an optimal control problem, which in turn is divided into a sequence of finite-dimensional problems. We derive conditions for the existence of solutions of these problems and the initial problem minimax estimation.