This article is cited in 4 papers

Approximate method for solving the boundary value problem for a parabolic equation with inhomogeneous transmission conditions of nonideal contact type

D. A. Nomirovskii

Faculty of Cybernetics, National University of Kiev, pr. Glushkova 6, Kiev, 03022, Ukraine

Abstract: A linear parabolic equation in a disconnected domain with inhomogeneous transmission conditions of the nonideal contact type is studied. A generalized formulation of the problem is considered. An analogue of the Galerkin method is proposed for solving the problem, and the stability of the method is investigated. This makes it possible to prove existence and uniqueness theorems for the equation under different assumptions on the data smoothness.

Key words: parabolic equation, Galerkin method, transmission conditions, nonideal contact, solvability, generalized functions.

UDC: 519.633

Received: 26.01.2004
Revised: 13.12.2005

 English version: Computational Mathematics and Mathematical Physics, 2006, 46:6, 995–1006

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