Сфералық қабаттағы және тордың iшкi бөлiгiндегi Моисил–Теодореско жүйесi үшiн Шварц есебi туралы
DOI:
https://doi.org/10.26577/JMMCS.2022.v114.i2.04Кілттік сөздер:
Коши–Риман жүйесi, Моисил–Теодореско жүйесi, Шварц есебi, сфералық қабат, тордың iшкi бөлiгi, есептiң шешiмдiлiгiАннотация
Екі байланысты облыстар сұйықтықтар механикасында маңызды рөл атқарады. Мысалы, өз осімен нормаль бағытта қозғалатын ұзын тұтас цилиндрден жасалған ағын дәл екі байланысты облыста жүзеге асады.
Бұл жұмыста сфералық қабаттағы және тордың ішкі бөлөлігіндегі Моисил - Теодореско жүйесі үшін тиянақты есептер келтірілген. Моисил--Теодореско жүйесі эллиптикалық Коши - Риман жүйесінің жалпыланған мысалы болып табылады. Бұл жұмыстың нәтижелерінен сфералық қабаттағы тиянақты қойылған есеп пен тордың ішкі бөлігінде қойылған есептің арасында айтарлықтай айырмашылықты көреміз.
Библиографиялық сілтемелер
[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
Жүктелулер
Как цитировать
Koshanov, B. D., Baiarystanov, A. O., Dosmagulova, K. A., Kuntuarova, A. D., & Sultangazieva, Z. B. (2022). Сфералық қабаттағы және тордың iшкi бөлiгiндегi Моисил–Теодореско жүйесi үшiн Шварц есебi туралы. Қазұу Хабаршысы. Математика, механика, информатика сериясы, 114(2). https://doi.org/10.26577/JMMCS.2022.v114.i2.04
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