Stationary Galerkin method for the semilinear nonclassical equation of higher order with alternating time direction

In a cylindrical domain $Q\subseteq \mathbb{R}^n$, we study a boundary value problem for the semilinear parabolic equation of odd order with alternating time direction. The theorem about the unique solvability of the boundary value problem is proved in the weighted Sobolev space. The stationary Galerkin method is applied to solve the problem and the error estimation for this method is obtained.