On convergence of the iterative process for the third order pseudo-parabolic equation with nonlocal boundary value conditions in a multidimensional domain

In this paper the nonlocal boundary value problem for the pseudo-parabolic equation of the third-order in a multidimensional domain is considered. Using an iterative method, the solving process of the nonlocal boundary value problem is reduced to solving the series of some local problems. An a priori estimate for the convergence of the iterative method in the norm $W^1_2(G)$ is obtained.