Information on the thesis

The thesis is dedicated to investigation of the well-posedness of problems for
parabolic equations and coupled systems of equations with time-dependent delay.
The conditions of existence and uniqueness of classical solutions of initial-
boundary problems for semilinear parabolic equations and coupled systems with
local variable delay, of problems without initial conditions for semilinear parabolic
equations and coupled systems with local variable delay are investigated.
The existence and uniqueness of weak solutions of problems for weakly nonli-
near parabolic equations with time-dependent integral delay are studied. The
conditions of well-posedness of initial-boundary problems and the problem wi-
thout initial conditions for such equations are obtained.
The conditions of existence and uniqueness of weak solutions of initial-boundary
problems for parabolic equations with variable exponents of nonlinearity and with
time-dependent integral delay are obtained. The conditions of existence and uni-
queness of weak solutions of the problem without initial conditions for parabolic
equations with variable exponents of nonlinearity and time-dependent integral
delay in unbounded on time domains in classes of functions with certain behavi-
or on innity are established. The well-posedness of the problem without initial
conditions for strongly nonlinear evolutional variation inequalities (subdierential
inclusions) with time-dependent integral delay in unbounded on time domains is
investigated in classes of functions with certain behavior on innity is established.

Key words: initial-boundary problem, problem without initial condition, time
delay, parabolic equation, coupled system, evolution equation, evolutional variati-
on inequality, evolution subdierential inclusion, strongly degenerated equation.