A priori estimates of the solutions of nonlocal boundary value problems for a pseudo-parabolic equation

In this paper we consider nonlocal boundary value problems for a third order pseudo-parabolic equation with variable coefficients in the one-dimensional and multidimensional cases. For nonlocal problems a priori estimates in differential and difference treatment are obtained. These estimates imply uniqueness, stability and convergence of the solution of the difference problem to the solution of the differential problem.