An approximate solution by the Galerkin method of a quasilinear equation with a boundary condition containing the time derivative of the unknown function

In the paper, we consider one boundary value problem of parabolic type with a divergent principal part when the boundary condition contains the time derivative of the unknown function with the dimension of the domain m ≥ 3. An approximate solution of the considered problem is constructed by the Galerkin method. The existence and uniqueness of a generalized solution of the problem is proved in the space H˜1,1(QT).