О задаче Шварца для системы Моисила–Теодореску в шаровом слое и во внутренности тора
DOI:
https://doi.org/10.26577/JMMCS.2022.v114.i2.04Ключевые слова:
система Коши–Римана, система Моисила–Теодореску, задача Шварца, шаровой слой, внутренность тора, разрешимость задачиАннотация
Двусвязные области играют значительную роль в механике жидкости. К примеру течение, создаваемое длинным твердым цилиндром, движущегося в направлении нормали к своей оси, происходит именно в двусвязной области.
В данной работе приведены корректные задачи для системы Моисила--Теодореску в случае шарового слоя и внутренности тора. Эллиптическая система Моисила--Теодореску является примером многомерной обобщенной системой Коши--Римана. Из результатов данной работы видно существенное отличие корректной задачи в шаровом слое от аналогичной задачи в торе.
Библиографические ссылки
[1] Batchelor G.K., An Introduction to Fluid Dynamics, Cambridge University Press. 2000.
[2] Hatcher A., Algebraic Topology, Cambridge University Press. New Yourk. 2002.
[3] Simmons G.F., Introduction to Topology and Modern Analysis, McGraw Hill Book Company. 1968.
[4] Agmon S., Douglis A., Nirenberg L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure and Appl. Math., 17 (1964), 35—92.
[5] Shevchenko V.I., Some boundary value problem for holomorphic vector, Sborn. Math. Phys. Kiev, 8 (1970), 172—187. (in Russian)
[6] Yao Y., The Riemann boundary value problem for the Moisil-Theodorescu system, In Tournal-Sichuan Normal University. Natural Science Edition, 29 (2006), 188—191.
[7] Soldatov A.P., The Riemann-Hilbert problem for the Moisil-Theodorescu system, Izv. RAN, Ser. Math. (2018) (in
Russian).
[8] Polunin V.A., Soldatov A.P., Riemann-Hilbert problem for the Moisil-Teodorescu system in multiply connected domains, Electronic Journal of Differential Equations, 310 (2016), 1–5.
[9] Polunin V.A., Soldatov A.P., On the integral represenation of solutions of the Moisil-Theodorescu system in multiply connected domains, Dokl. RAN, 475:4 (2017), 192–201.
[10] Moisil Gr. C., Theodoresco N., Fonctions holomorphes dans l’espace, Mathematica, 5 (1931), 142-153.
[11] Stein I., Weiss G., Introduction to harmonic analysis on Euclidean spaces, Moscow. Mir. 1974.
[12] Bitsadze A.V., Spatial analogue of the Cauchy-type integral and some of its applications, Izv. USSR Academy of Sciences, ser. math., 17:6 (1953), 525-538.
[13] Bitsadze A.V., Boundary value problems for second order elliptic equations, Moscow. Mir. 1966.
[14] Polunin V.A., Soldatov A.P., Three-dimensional analogue of the Cauchy-type integral, Differ. equations, 47:3 (2011), 366-375.
[15] Nazarov S., Plamenevsky B.A., Elliptic problems in domains with piecewise smooth boundaries. Walter de Gruyter, 2011.
[16] Kozhanov A.I., Koshanov B.D., Sultangazieva Zh.B., New boundary value problems for fourth-order quasi-hyperbolic equations, Siberian Electronic Mathematical Reports, 16 (2019), 1383-1409. http://dx.doi.org/10.33048/semi.2019.16.098
[17] Koshanov B.D., Soldatov A.P., Boundary value problem with normal derivatives for a higher order elliptic equation on the plane, Differential Equations, 52:12 (2016), 1594-1609. https://doi.org/10.1134/S0012266116120077
[18] Koshanov B.D., Soldatov A.P., On the Solvability of the Boundary Value Problems for the Elliptic Equation
of High Order on a Plane, Bulletin of the Karaganda University. Mathematics series, 91:3 (2018), 24-31.
https://doi.org/10.31489/2018M3/24-30
[19] Koshanov B.D., Equivalence of the Fredholm solvability condition for the Neumann problem to the
complementarity condition, Journal of Mathematics, Mechanics and Computer Science, 109:1 (2021), 34-54.
https://doi.org/10.26577/JMMCS.2021.v111.i3.04
[2] Hatcher A., Algebraic Topology, Cambridge University Press. New Yourk. 2002.
[3] Simmons G.F., Introduction to Topology and Modern Analysis, McGraw Hill Book Company. 1968.
[4] Agmon S., Douglis A., Nirenberg L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure and Appl. Math., 17 (1964), 35—92.
[5] Shevchenko V.I., Some boundary value problem for holomorphic vector, Sborn. Math. Phys. Kiev, 8 (1970), 172—187. (in Russian)
[6] Yao Y., The Riemann boundary value problem for the Moisil-Theodorescu system, In Tournal-Sichuan Normal University. Natural Science Edition, 29 (2006), 188—191.
[7] Soldatov A.P., The Riemann-Hilbert problem for the Moisil-Theodorescu system, Izv. RAN, Ser. Math. (2018) (in
Russian).
[8] Polunin V.A., Soldatov A.P., Riemann-Hilbert problem for the Moisil-Teodorescu system in multiply connected domains, Electronic Journal of Differential Equations, 310 (2016), 1–5.
[9] Polunin V.A., Soldatov A.P., On the integral represenation of solutions of the Moisil-Theodorescu system in multiply connected domains, Dokl. RAN, 475:4 (2017), 192–201.
[10] Moisil Gr. C., Theodoresco N., Fonctions holomorphes dans l’espace, Mathematica, 5 (1931), 142-153.
[11] Stein I., Weiss G., Introduction to harmonic analysis on Euclidean spaces, Moscow. Mir. 1974.
[12] Bitsadze A.V., Spatial analogue of the Cauchy-type integral and some of its applications, Izv. USSR Academy of Sciences, ser. math., 17:6 (1953), 525-538.
[13] Bitsadze A.V., Boundary value problems for second order elliptic equations, Moscow. Mir. 1966.
[14] Polunin V.A., Soldatov A.P., Three-dimensional analogue of the Cauchy-type integral, Differ. equations, 47:3 (2011), 366-375.
[15] Nazarov S., Plamenevsky B.A., Elliptic problems in domains with piecewise smooth boundaries. Walter de Gruyter, 2011.
[16] Kozhanov A.I., Koshanov B.D., Sultangazieva Zh.B., New boundary value problems for fourth-order quasi-hyperbolic equations, Siberian Electronic Mathematical Reports, 16 (2019), 1383-1409. http://dx.doi.org/10.33048/semi.2019.16.098
[17] Koshanov B.D., Soldatov A.P., Boundary value problem with normal derivatives for a higher order elliptic equation on the plane, Differential Equations, 52:12 (2016), 1594-1609. https://doi.org/10.1134/S0012266116120077
[18] Koshanov B.D., Soldatov A.P., On the Solvability of the Boundary Value Problems for the Elliptic Equation
of High Order on a Plane, Bulletin of the Karaganda University. Mathematics series, 91:3 (2018), 24-31.
https://doi.org/10.31489/2018M3/24-30
[19] Koshanov B.D., Equivalence of the Fredholm solvability condition for the Neumann problem to the
complementarity condition, Journal of Mathematics, Mechanics and Computer Science, 109:1 (2021), 34-54.
https://doi.org/10.26577/JMMCS.2021.v111.i3.04
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Как цитировать
Koshanov, B. D., Baiarystanov, A. O., Dosmagulova, K. A., Kuntuarova, A. D., & Sultangazieva, Z. B. (2022). О задаче Шварца для системы Моисила–Теодореску в шаровом слое и во внутренности тора. Вестник КазНУ. Серия математика, механика, информатика, 114(2). https://doi.org/10.26577/JMMCS.2022.v114.i2.04
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Математика
