An approximation scheme for a nonlinear degenerate parabolic equation with a second-order differential Volterra operator

A nonlinear degenerate parabolic initial boundary value problem with a second-order differential Volterra operator is studied. The approximate solution is found due to the semi-discretization in time which is based on Rotheʹs method. The convergence of the approximation scheme, existence and uniqueness of solution as well as some regularity results are proved.