Bokalo M. Problems without initial conditions for first-order in time evoltion equations

In the thesis the questions of existence, uniqueness and continuous dependence on initial data of solutions to the boundary value problems without initial conditions are considered for variuos classes of evolution equations with the first time derivative and different properties of such solutions are also studied. The classes of essentially nonlinear parabolic equations in bounded with respect to space variables domains are singled out for which the corresponding problems without initial conditions (the Fourier problems) are well-posed and no additional conditions on the solution behaviour and increasing of initial data at infinity are required.