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This article is cited in 20 scientific papers (total in 20 papers)
Construction of polynomial solutions to the Dirichlet problem for the polyharmonic equation in a ball
V. V. Karachik
Southern Ural State University, pr. Lenina 76, Chelyabinsk, 454080, Russia
Abstract:
An algorithm is proposed for the analytical construction of a polynomial solution to Dirichlet problem for an inhomogeneous polyharmonic equation with a polynomial right-hand side and polynomial boundary data in the unit ball.
Key words:
polyharmonic equation, Almansi formula, polyharmonic polynomials, Dirichlet problem, polynomial solutions.
DOI:
https://doi.org/10.7868/S0044466914070072
 Full text:
PDF file (341 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:7, 1122–1143
Bibliographic databases:
    
UDC:
519.632
MSC: 35J40,35B30
Received: 10.12.2013
Revised: 23.01.2014
Citation:
V. V. Karachik, “Construction of polynomial solutions to the Dirichlet problem for the polyharmonic equation in a ball”, Zh. Vychisl. Mat. Mat. Fiz., 54:7 (2014), 1149–1170; Comput. Math. Math. Phys., 54:7 (2014), 1122–1143
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/zvmmf10064 http://mi.mathnet.ru/eng/zvmmf/v54/i7/p1149
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
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This publication is cited in the following articles:
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I. A. Gulyaschikh, “Zadacha Neimana dlya poligarmonicheskogo uravneniya v edinichnom share”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 7:2 (2015), 70–72
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V. V. Karachik, M. A. Sadybekov, B. T. Torebek, “Uniqueness of solutions to boundary-value problems for the biharmonic equation in a ball”, Electron. J. Differ. Equ., 2015, 244
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I. A. Gulyaschikh, “Odnorodnaya zadacha Dirikhle–Rike dlya neodnorodnogo bigarmonicheskogo uravneniya v share”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 8:1 (2016), 57–60
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V. V. Karachik, “A Neumann-type problem for the biharmonic equation”, Siberian Adv. Math., 27:2 (2017), 103–118
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V. V. Karachik, B. T. Torebek, “On one mathematical model described by boundary value problem for the biharmonic equation”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:4 (2016), 40–52
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V. V. Karachik, B. T. Torebek, “On uniqueness and correct solvability of the biharmonic boundary value problem”, International Conference on Analysis and Applied Mathematics (ICAAM 2016) (Almaty, Kazakhstan, 7–10 September 2016), AIP Conf. Proc., 1759, eds. A. Ashyralyev, A. Lukashov, Amer. Inst. Phys., 2016, 020045
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B. Kh. Turmetov, V. V. Karachik, “About one boundary value problem for the biharmonic equation”, Applications of Mathematics in Engineering and Economics (AMEE'16), AIP Conf. Proc., 1789, eds. V. Pasheva, N. Popivanov, G. Venkov, Amer. Inst. Phys., 2016, UNSP 040015
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B. Kh. Turmetov, “On the solvability of some boundary value problems for the inhomogeneous polyharmonic equation with boundary operators of the Hadamard type”, Differ. Equ., 53:3 (2017), 333–344
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V. V. Karachik, B. T. Torebek, “On the Dirichlet–Riquier Problem for Biharmonic Equations”, Math. Notes, 102:1 (2017), 31–42
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V. V. Karachik, “Zadacha tipa Neimana dlya poligarmonicheskogo uravneniya v share”, Chelyab. fiz.-matem. zhurn., 2:4 (2017), 420–429
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V. Karachik, B. Turmetov, “Solvability of some Neumann-type boundary value problems for biharmonic equations”, Electron. J. Differ. Equ., 2017, 218
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V. V. Karachik, “Integralnye tozhdestva na sfere dlya normalnykh proizvodnykh poligarmonicheskikh funktsii”, Sib. elektron. matem. izv., 14 (2017), 533–551
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V. V. Karachik, “Riquier–Neumann problem for the polyharmonic equation in a ball”, Differ. Equ., 54:5 (2018), 648–657
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B. Turmetov, V. Karachik, “On solvability of some boundary value problems for a biharmonic equation with periodic conditions”, Filomat, 32:3 (2018), 947–953
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V. V. Karachik, B. Kh. Turmetov, “On the Green's function for the third boundary value problem”, Siberian Adv. Math., 29:1 (2019), 32–43
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V. V. Karachik, “Ob odnom predstavlenii funktsii Grina zadachi Dirikhle dlya bigarmonicheskogo uravneniya v share”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 10:4 (2018), 13–22
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B. Kh. Turmetov, “On Green's function of certain boundary-value problems for the biharmonic equation”, International Conference on Analysis and Applied Mathematics (ICAAM 2018), AIP Conf. Proc., 1997, eds. A. Ashyralyev, A. Lukashov, M. Sadybekov, Amer. Inst. Phys., 2018, 020056-1
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Karachik V., “Green'S Function of Dirichlet Problem For Biharmonic Equation in the Ball”, Complex Var. Elliptic Equ., 64:9 (2019), 1500–1521
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Karachik V.V., Turmetov B.K., “On Green'S Function of the Robin Problem For the Poisson Equation”, Adv. Pure Appl. Math., 10:3 (2019), 203–213
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V. V. Karachik, “The Green Function of the Dirichlet Problem for the Triharmonic Equation in the Ball”, Math. Notes, 107:1 (2020), 105–120
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