Procedings of the 3nd International Conference "Mathematical Physics and its Applications"
Equations of Mathematical Physics

On convergence of the iterative process for the third order pseudo-parabolic equation with nonlocal boundary value conditions in a multidimensional domain

M. H. Beshtokov

Kabardino-Balkar State University, Nalchik, 360004, Russia

Abstract: In this paper the nonlocal boundary value problem for the pseudo-parabolic equation of the third-order in a multidimensional domain is considered. Using an iterative method, the solving process of the nonlocal boundary value problem is reduced to solving the series of some local problems. An a priori estimate for the convergence of the iterative method in the norm $W^1_2(G)$ is obtained.

Keywords: boundary value problems, nonlocal condition, a priori estimate, iteration process, third order equation, pseudo-parabolic equation.

UDC: 519.635

MSC: Primary 35S15; Secondary 47G30

Original article submitted 29/III/2013
revision submitted – 01/IV/2013

DOI: 10.14498/vsgtu1234

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