Ilnytska O. Problems without initial conditions for evolution systems with delay

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 and 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 nonlinear parabolic equations with time-dependent integral delay are studied. The conditions of existence and uniqueness of weak solutions of initial-boundary problems and problem without initial conditions for parabolic equations with variable exponents of nonlinearity and with time-dependent integral delay are obtained. The well-posedness of the problem without initial conditions for strongly nonlinear evolutional subdifferential inclusions with time-dependent integral delay in unbounded on time domains is investigated.