Tsebenko A. Optimal control in problems without initial conditions for evolution equations and variational inequalities

The thesis is dedicated to the investigation of the optimal control problems for systems governed by evolution equations and variational inequalities without initial conditions.Necessary and sufficient conditions for existence of an optimal coefficient control in the problem without initial conditions for weakly nonlinear parabolic equations are examined. The sufficient conditions for existence of an optimal control in the case when the state of controlled system is governed by Fourier problem for strongly nonlinear equations with monotone and non-monotone spatial parts are investigated. The conditions for existence of the solutions of an optimal control problem for systems governed by Fourier problems for variational inequalities with controls in the right-hand side and in the coefficients are established. The control problem for a linear parabolic equations strongly degenerated at the initial moment controlled by the right-hand side of the equation are studied.