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Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2011, Volume 11, Issue 4, Pages 34–40 (Mi isu264)  

This article is cited in 4 scientific papers (total in 4 papers)

Mathematics

Finding of accessory parameters for mixed inverse boundary value problem with polygonal known part of boundary

S. R. Nasyrova, L. Yu. Nizamievab

a Kazan (Volga Region) Federal University, Chair of Mathematical Analysis
b Kazan National Research Technical University, Chair of Computing Mathematics

Abstract: We consider a mixed inverse boundary value problem with respect to parameter $x$ for the case when the known part of the boundary $L_z^1$ is a polygonal line. Integral representation of solution to the problem depends on real parameters being the pre-images of the vertices of $L_z^1$ under conformal mapping. By analogy with Schwartz–Christoffel integrals, we name them accessory parameters. It is suggested a new method of determining the accessory parameters. Is is based on consideration of one-parametric family of solutions to the problem corresponding to the case when the known part of the boundary is the union of two rays and the stretching slit the endpoint of which goes along the given polygonal line $L_z^1$.

Key words: boundary value problems with free boundary, Hilbert boundary value problem, accessory parameters.

DOI: https://doi.org/10.18500/1816-9791-2011-11-4-34-40

Full text: PDF file (186 kB)
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UDC: 517.5

Citation: S. R. Nasyrov, L. Yu. Nizamieva, “Finding of accessory parameters for mixed inverse boundary value problem with polygonal known part of boundary”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 11:4 (2011), 34–40

Citation in format AMSBIB
\Bibitem{NasNiz11}
\by S.~R.~Nasyrov, L.~Yu.~Nizamieva
\paper Finding of accessory parameters for mixed inverse boundary value problem with polygonal known part of boundary
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2011
\vol 11
\issue 4
\pages 34--40
\mathnet{http://mi.mathnet.ru/isu264}
\crossref{https://doi.org/10.18500/1816-9791-2011-11-4-34-40}


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    This publication is cited in the following articles:
    1. I. A. Kolesnikov, “Opredelenie aktsessornykh parametrov dlya otobrazheniya na schetnougolnik”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2014, no. 2(28), 18–28  mathnet
    2. I. A. Kolesnikov, “On the problem of determining parameters in the Schwarz equation”, Probl. anal. Issues Anal., 7(25), spetsvypusk (2018), 50–62  mathnet  crossref  elib
    3. I. A. Kolesnikov, “Opredelenie aktsessornykh parametrov konformnykh otobrazhenii iz verkhnei poluploskosti na pryamolineinye schetnougolniki s dvoinoi simmetriei i krugovye schetnougolniki”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2019, no. 60, 42–60  mathnet  crossref  elib
    4. I. A. Kolesnikov, “Nakhozhdenie parametrov konformnogo otobrazheniya iz poluploskosti na krugovoi mnogougolnik”, MaterialyXVII Vserossiiskoi molodezhnoishkoly-konferentsii Lobachevskie chteniya-2018,23-28 noyabrya 2018 g., Kazan.Chast 1, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 175, VINITI RAN, M., 2020, 56–68  mathnet  crossref
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