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University proceedings. Volga region. Physical and mathematical sciences, 2012, Issue 1, Pages 92–102 (Mi ivpnz512)  
Mathematics

The method of integral equations for solving the Dirichlet problem in a perturbed three-dimensional layer

Yu. G. Smirnov, A. A. Shcherbakov, A. V. Cvetkov

Penza State University, Penza
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Abstract: A Dirichlet boundary value problem for the Laplace equation in a three-dimensional layer with a local perturbation of the boundary is solved by the method of boundary integral equation (IE). The unique solvability of the IE and its Fredholm property are proved. A Galerkin method of the IE numerical solution aimed at the use of parallel computations is developed and justified.
Keywords: perturbed layer, boundary integral equation, Galerkin method.
Document Type: Article
UDC: 517.3
Language: Russian
Citation: Yu. G. Smirnov, A. A. Shcherbakov, A. V. Cvetkov, “The method of integral equations for solving the Dirichlet problem in a perturbed three-dimensional layer”, University proceedings. Volga region. Physical and mathematical sciences, 2012, no. 1, 92–102
Citation in format AMSBIB
\Bibitem{SmiShcCve12}
\by Yu.~G.~Smirnov, A.~A.~Shcherbakov, A.~V.~Cvetkov
\paper The method of integral equations for solving the Dirichlet problem in a perturbed three-dimensional layer
\jour University proceedings. Volga region. Physical and mathematical sciences
\yr 2012
\issue 1
\pages 92--102
\mathnet{http://mi.mathnet.ru/ivpnz512}
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