Abstract:
A nonlocal boundary value problem for a third-order hyperbolic equation with variable coefficients is considered in the one- and multidimensional cases. A priori estimates for the nonlocal problem are obtained in the differential and difference formulations. The estimates imply the stability of the solution with respect to the initial data and the right-hand side on a layer and the convergence of the difference solution to the solution of the differential problem.
Key words:boundary value problems, nonlocal condition, a priori estimate, difference scheme, stability and convergence of difference schemes, third-order hyperbolic equation, pseudo-parabolic equation.
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