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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 7, Pages 1149–1170 (Mi zvmmf10064)  

This article is cited in 17 scientific papers (total in 17 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)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2014, 54:7, 1122–1143

Bibliographic databases:

Document Type: Article
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

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  mathnet  elib
    2. 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  mathscinet  zmath  isi  elib
    3. 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  mathnet  crossref  elib
    4. V. V. Karachik, “A Neumann-type problem for the biharmonic equation”, Siberian Adv. Math., 27:2 (2017), 103–118  mathnet  crossref  crossref  elib
    5. 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  mathnet  crossref  elib
    6. 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  crossref  isi  scopus
    7. 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  crossref  isi  scopus
    8. 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  crossref  isi  elib
    9. V. V. Karachik, B. T. Torebek, “On the Dirichlet–Riquier Problem for Biharmonic Equations”, Math. Notes, 102:1 (2017), 31–42  mathnet  crossref  crossref  mathscinet  isi  elib
    10. V. V. Karachik, “Zadacha tipa Neimana dlya poligarmonicheskogo uravneniya v share”, Chelyab. fiz.-matem. zhurn., 2:4 (2017), 420–429  mathnet  mathscinet  elib
    11. V. Karachik, B. Turmetov, “Solvability of some Neumann-type boundary value problems for biharmonic equations”, Electron. J. Differ. Equ., 2017, 218  mathscinet  zmath  isi
    12. V. V. Karachik, “Integralnye tozhdestva na sfere dlya normalnykh proizvodnykh poligarmonicheskikh funktsii”, Sib. elektron. matem. izv., 14 (2017), 533–551  mathnet  crossref  mathscinet  zmath
    13. V. V. Karachik, “Riquier-Neumann problem for the polyharmonic equation in a ball”, Differ. Equ., 54:5 (2018), 648–657  crossref  isi  scopus
    14. B. Turmetov, V. Karachik, “On solvability of some boundary value problems for a biharmonic equation with periodic conditions”, Filomat, 32:3 (2018), 947–953  crossref  mathscinet  isi  scopus
    15. V. V. Karachik, B. Kh. Turmetov, “O funktsii Grina tretei kraevoi zadachi dlya uravneniya Puassona”, Matem. tr., 21:1 (2018), 17–34  mathnet  crossref
    16. 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  mathnet  crossref
    17. Turmetov B.Kh., “On Green'S Function of Certain Boundary-Value Problems For the Biharmonic Equation”, AIP Conference Proceedings, 1997, eds. Ashyralyev A., Lukashov A., Sadybekov M., Amer Inst Physics, 2018, UNSP 020056-1  crossref  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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