On a Boundary Value Problem for a Pseudo-Parabolic Equation of the Third Order with a Nonlocal Condition
A nonlocal boundary value problem for the third order pseudo-parabolic equation with variable coefficients is considered. For solving the nonlocal boundary value problem by the method of energy inequalities in the class of sufficiently smooth coefficients and boundary conditions, a priori estimates in differential and difference setting are obtained. The obtained a priori estimates imply uniqueness and stability of the solution of the problem with respect to the initial data and the right-hand side, and also the convergence of the solution of the difference problem to the solution of the differential problem at the rate  in the norm  on each layer.