Paliyenko L. Simulation and generalized optimization in the pseudohyperbolic systems

The dissertation is devoted to study of mathematical simulation, construction of numerical methods and optimal control (including point-impulse) in systerms which are described by the pseudohyperbolic equations. The investigation is conducted on the basis of thr equipped Hilbert spaces theory and inequalities with negative norms. It is proved that the problem has unique generalized solution which belohgs to the positive Hilbert space. The effective Galyorkin type method of approximate solution structure is suggested. It is demonstrated the existence of optimal control and applicability of gradient method to find it.