A priori estimates of the solutions of nonlocal boundary value problems for a pseudoparabolic equation. (Russian. English summary) Zbl 1288.35321

Beshtokov, M. H.

Vladikavkaz. Mat. Zh. 15, No. 3, 19-36 (2013).

Summary: 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.

MSC:

35K70	Ultraparabolic equations, pseudoparabolic equations, etc.
35K20	Initial-boundary value problems for second-order parabolic equations
35B45	A priori estimates in context of PDEs
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs

Keywords:

nonlocal condition; difference scheme; stability and convergence of difference schemes; hyperbolic equation of the third order