This article is cited in 2 scientific papers (total in 2 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
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.
parabolic equation, Galerkin method, transmission conditions, nonideal contact, solvability, generalized functions.
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Computational Mathematics and Mathematical Physics, 2006, 46:6, 995–1006
D. A. Nomirovskii, “Approximate method for solving the boundary value problem for a parabolic equation with inhomogeneous transmission conditions of nonideal contact type”, Zh. Vychisl. Mat. Mat. Fiz., 46:6 (2006), 1045–1057; Comput. Math. Math. Phys., 46:6 (2006), 995–1006
Citation in format AMSBIB
\paper Approximate method for solving the boundary value problem for a~parabolic equation with inhomogeneous transmission conditions of nonideal contact type
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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This publication is cited in the following articles:
Nomirovskii D., “Generalized solvability and optimization of a parabolic system with a discontinuous solution”, J. Differential Equations, 233:1 (2007), 1–21
Nomirovskii D.A., Vostrikov O.I., “Generalized Statements and Properties of Models of Transport Processes in Domains with Cuts”, Cybern. Syst. Anal., 52:6 (2016), 931–942
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