Respondent

Tsebenko Andriy Mykolayovych

Theme

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

Annotation

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 sucient conditions for existence of an opti-
mal coecient control in the problem without initial conditions for weakly nonli-
near parabolic equations are examined. The sucient conditions for existence of
an optimal control in the case when the state of controlled system is governed24
by Fourier problem for strongly nonlinear equations with monotone and non-
monotone spatial parts are investigated. The conditions for existence of the soluti-
ons of an optimal control problem for systems governed by Fourier problems for
variational inequalities with controls in the right-hand side and in the coecients
are established. The control problem for a linear parabolic equations strongly
degenerated at the initial moment controlled by the right-hand side of the equati-
on are studied. Necessary and sucient conditions for existence of an optimal
control are proved.
Key words: parabolic equation, evolution equation, degenerated parabolic
equation, parabolic variational inequality, evolutionary variational inequality,
problem without initial condition, optimal control, optimal control problem.

Defence Date

29.06.2017

Dissertation File

Autosummary File