On uniqueness of the solution of a variational inequality of the coupled movement of the underground and surface waters theory with nonhomogeneous bounds and nonhomogeneous boundary conditions

The considered problem is a double degenerate problem. The special feature of the investigated problem is also the nonlocal boundary condition on the inner slit of the domain. The uniqueness theorem for the first boundary value problem for variational inequality with nonhomogeneous bound on the solution is proved.