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Matematicheskie Trudy, 2016, Volume 19, Number 2, Pages 86–108
DOI: https://doi.org/10.17377/mattrudy.2016.19.203
(Mi mt306)
 

This article is cited in 28 scientific papers (total in 28 papers)

A Neumann-type problem for the biharmonic equation

V. V. Karachik

South Ural State University, Chelyabinsk, Russia
References:
Abstract: We establish the existence and uniqueness of a solution to a Neumann-type problem in the unit ball. An illustrative example is considered.
Key words: biharmonic equation, Neumann-type problem, solvability condition.
Received: 06.04.2016
English version:
Siberian Advances in Mathematics, 2017, Volume 27, Issue 2, Pages 103–118
DOI: https://doi.org/10.3103/S105513441702002X
Bibliographic databases:
Document Type: Article
UDC: 517.575+519.635.4
Language: Russian
Citation: V. V. Karachik, “A Neumann-type problem for the biharmonic equation”, Mat. Tr., 19:2 (2016), 86–108; Siberian Adv. Math., 27:2 (2017), 103–118
Citation in format AMSBIB
\Bibitem{Kar16}
\by V.~V.~Karachik
\paper A Neumann-type problem for the biharmonic equation
\jour Mat. Tr.
\yr 2016
\vol 19
\issue 2
\pages 86--108
\mathnet{http://mi.mathnet.ru/mt306}
\crossref{https://doi.org/10.17377/mattrudy.2016.19.203}
\elib{https://elibrary.ru/item.asp?id=27258779}
\transl
\jour Siberian Adv. Math.
\yr 2017
\vol 27
\issue 2
\pages 103--118
\crossref{https://doi.org/10.3103/S105513441702002X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85020053019}
Linking options:
  • https://www.mathnet.ru/eng/mt306
  • https://www.mathnet.ru/eng/mt/v19/i2/p86
  • This publication is cited in the following 28 articles:
    1. V. V. Karachik, “Reshenie zadachi Rike-Neimana dlya poligarmonicheskogo uravneniya v share”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 15:1 (2023), 26–33  mathnet  crossref
    2. V. V. Karachik, “Representation of the Green's Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball”, Diff Equat, 59:8 (2023), 1061  crossref
    3. Valery Karachik, “Riquier–Neumann Problem for the Polyharmonic Equation in a Ball”, Mathematics, 11:4 (2023), 1000  crossref
    4. Karachik V., “Green'S Functions of Some Boundary Value Problems For the Biharmonic Equation”, Complex Var. Elliptic Equ., 67:7 (2022), 1712–1736  crossref  mathscinet  isi  scopus
    5. B. Kh. Turmetov, V. V. Karachik, “Zadacha Neimana dlya nelokalnogo bigarmonicheskogo uravneniya”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 14:2 (2022), 51–58  mathnet  crossref
    6. V. V. Karachik, “Solution to the Dirichlet Problem for the Polyharmonic Equation in the Ball”, Sib. Adv. Math., 32:3 (2022), 197  crossref
    7. V. V. Karachik, “Reshenie zadachi Dirikhle dlya poligarmonicheskogo uravneniya v share”, Matem. tr., 24:2 (2021), 46–64  mathnet  crossref
    8. V. Karachik, “Dirichlet and Neumann boundary value problems for the polyharmonic equation in the unit ball”, Mathematics, 9:16 (2021), 1907  crossref  mathscinet  isi  scopus
    9. V. V. Karachik, “Green's functions of the Navier and Riquier-Neumann problems for the biharmonic equation in the ball”, Differ. Equ., 57:5 (2021), 654–668  crossref  mathscinet  isi  scopus
    10. Batirkhan Turmetov, Valery Karachik, INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020, 2365, INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020, 2021, 060002  crossref
    11. V. V. Karachik, “Sufficient conditions for solvability of one class of Neumann-type problems for the polyharmonic equation”, Comput. Math. Math. Phys., 61:8 (2021), 1276–1288  mathnet  mathnet  crossref  crossref  isi  scopus
    12. Valery V. Karachik, Batirkhan Kh. Turmetov, Springer Proceedings in Mathematics & Statistics, 351, Functional Analysis in Interdisciplinary Applications—II, 2021, 75  crossref
    13. V. V. Karachik, “Usloviya razreshimosti zadachi Neimana N2 dlya poligarmonicheskogo uravneniya v share”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 12:2 (2020), 13–20  mathnet  crossref
    14. V. V. Karachik, “Class of Neumann-type problems for the polyharmonic equation in a ball”, Comput. Math. Math. Phys., 60:1 (2020), 144–162  mathnet  crossref  crossref  isi  elib
    15. V. V. Karachik, “Neumann Type Problems for the Polyharmonic Equation in Ball”, J Math Sci, 249:6 (2020), 974  crossref
    16. Valery Karachik, Batirkhan Turmetov, “On solvability of some nonlocal boundary value problems for biharmonic equation”, Mathematica Slovaca, 70:2 (2020), 329  crossref
    17. V. V. Karachik, “The Green function of the Dirichlet problem for the biharmonic equation in a ball”, Comput. Math. Math. Phys., 59:1 (2019), 66–81  mathnet  crossref  crossref  isi  elib
    18. Valery Karachik, “Green's function of Dirichlet problem for biharmonic equation in the ball”, Complex Variables and Elliptic Equations, 64:9 (2019), 1500  crossref
    19. Valery V. Karachik, Batirkhan K. Turmetov, “On Green's function of the Robin problem for the Poisson equation”, Advances in Pure and Applied Mathematics, 10:3 (2019), 203  crossref
    20. Djumaklich Amanov, Gafurjan Ibragimov, Adem K{\i}lıçman, “On a Generalization of the Initial-Boundary Problem for the Vibrating String Equation”, Symmetry, 11:1 (2019), 73  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические труды Siberian Advances in Mathematics
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