Trofymchuk O. Optimal control problems for the systems of integral - differential equations with degenerate parabolicity.

Dissertation work is devoted the theoretical analysis of problems of optimal control for a Coshi problem and initial-boundary problems for the systems of integral-differential equations of parabolic type with a piece-smooth degenerate coefficient at the second deriva-tives and development of numeral methods of resolving of this problems. In the dissertation the sufficient conditions of existence and uniqueness of the com-mon solution of Coshi problem and initial-boundary problem for the system of multidimen-sional integral-differential equations with degenerate parabolicity are achieved. It was proved the sufficient terms for existence at least of one optimal control for the system of multidimensional integral-differential equations with degenerate parabolicity. It was established the limitations for the functional spaces of coefficients of integral-differential equations, initial and boundary conditions of optimal control problem. Using the integral-interpolation method, the splitting method and method of regularization of numerical schemes, it was created nonlinear monotonous schemes of the higher first order of exactness for a Coshi problem and initial-boundary problem for the system of one-dimensional integral-differential equations with degenerate parabolicity and for an initial-boundary problem for multidimensional integral- differential equation with degenerate parabolicity. On the basis of apriori estimations it was estimated the speed of convergence of numerical solution for each equations of the system to the exact solution. For the problem of optimal control of the system of initial-regional problem for multidimensional integral - differential equations it was created the stable numerical method of optimal control, based on the class of piece-smooth polynomial functions with the limited coefficients (on a compact set) for weakly semicontinuous from below functional of quality. On the basis of this approaches the stable numeral algorithm of optimal control is developed. Numeral calculations of the developed algorithm for two-dimensional integral-differential equations with degenerate parabolicity showed efficiency of using it in the on-line computing systems.