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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 11, Pages 1931–1936 (Mi zvmmf4780)  

Solution of boundary value problems for Laplace's equation in a piecewise homogeneous plane with a parabolic crack (screen)

S. E. Kholodovskii

Chernyshevsky Transbaikalian State Humanitarian and Pedagogical University, ul. Babushkina 129, Chita, 672007, Russia

Abstract: Boundary value problems for Laplace's equation are considered in a piecewise homogeneous plane divided into two zones by a strongly permeable crack or a weakly permeable screen in the form of a parabola. The desired potentials have prescribed singular points (sources, sinks, etc.). Formulas are derived expressing the potentials in terms of harmonic functions that have the given singular points and describe similar processes in a homogeneous plane.

Key words: problems of mathematical physics in piecewise homogeneous media, parabolic crack (screen), convolution of Fourier expansions, Laplace's equation.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:11, 1847–1852

Bibliographic databases:

UDC: 519.634
Received: 30.03.2009
Revised: 13.05.2009

Citation: S. E. Kholodovskii, “Solution of boundary value problems for Laplace's equation in a piecewise homogeneous plane with a parabolic crack (screen)”, Zh. Vychisl. Mat. Mat. Fiz., 49:11 (2009), 1931–1936; Comput. Math. Math. Phys., 49:11 (2009), 1847–1852

Citation in format AMSBIB
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\paper Solution of boundary value problems for Laplace's equation in a~piecewise homogeneous plane with a~parabolic crack (screen)
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2009
\vol 49
\issue 11
\pages 1931--1936
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\jour Comput. Math. Math. Phys.
\yr 2009
\vol 49
\issue 11
\pages 1847--1852
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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