Anikushyn A. Numerical methods for optimization and modelling of processes which describes by linear integral-differential equations

This thesis has received new science-based results in integro-differential equations and optimal control. The generalized solvability conditions of integral-differential operators with positive-defined integral operators formulated and proved. The existence of optimal control of the systems which have been described by the equations is proved. The existence of optimal control for systems described by equations of elliptic, parabolic or hyperbolic types is proved. The existence and uniqueness of generalized solution for operators satisfying the weakened a priori inequality are proved. The relationship between a priory inequalities and weak a priori inequalities is investigated.