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

Beshtokov, M. Kh.
Vladikavkaz Mathematical Journal 2013. Vol. 15. Issue 3.

Abstract:
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.

Keywords: boundary value problem, nonlocal condition, a priori estimate, difference scheme, stability and convergence of difference schemes, hyperbolic equation of the third order, pseudo-parabolic equation.

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