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Sibirskii Zhurnal Vychislitel'noi Matematiki
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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2017, Volume 20, Number 4, Pages 425–437
DOI: https://doi.org/10.15372/SJNM20170406 (Mi sjvm661) 		 
This article is cited in 7 scientific papers (total in 7 papers)

A boundary value problem for one overdetermined stationary system emerging in the two-velocity hydrodynamics

M. V. Urevabc, Kh. Kh. Imomnazarova, Jian-Gang Tangd

a Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 6 Lavrentiev av., Novosibirsk, 630090, Russia
b Novosibirsk State University, 2 Pirogova str., Novosibirsk, 630090, Russia
c Siberian Institute of Management — branch of the Russian Academy of National Economy and Public Service (RANE&PS), 6 Nizhegorodskya str., Novosibirsk, 630102, Russia
d YiLi Normal University, 448, Jiefang Road, Yinning Xinjiang, P.R. of China
Full-text PDF (559 kB) Citations (7)
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DOI: https://doi.org/10.15372/SJNM20170406
Abstract: In this paper we investigate the two-velocity stationary hydrodynamics system with a single pressure and inhomogeneous divergent and boundary conditions for the two velocities. This system is overdetermined. By replacing the unknown functions, the problem is reduced to a homogeneous one. The solution of the resulting system is reduced to the consecutive solutions of the two boundary value problems: the Stokes problem for a single velocity and pressure, and overdetermined system for the other velocity. We present the generalized statements of these problems and their discrete approximation using the finite element method. To solve the overdetermined problem we apply a version of the regularization methods.
Key words: overdetermined two-velocity stationary hydrodynamics system, Lagrange multiplier, finite element method.
Funding agency Grant number
Russian Foundation for Basic Research 14-11-00485П
Received: 10.01.2017
Revised: 18.05.2017
English version:
Numerical Analysis and Applications, 2017, Volume 10, Issue 4, Pages 347–357
DOI: https://doi.org/10.1134/S1995423917040061
Bibliographic databases:
Document Type: Article
UDC: 519.632
Language: Russian
Citation: M. V. Urev, Kh. Kh. Imomnazarov, Jian-Gang Tang, “A boundary value problem for one overdetermined stationary system emerging in the two-velocity hydrodynamics”, Sib. Zh. Vychisl. Mat., 20:4 (2017), 425–437; Num. Anal. Appl., 10:4 (2017), 347–357
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sjvm/v20/i4/p425
    • This publication is cited in the following 7 articles:
    1. M. Urev, R. Bahramov, Sh. Imomnazarov, I. Iskandarov, “External Boundary Value Problem for One Overdetermined System Arising in Two-Velocity Hydrodynamics”, J Math Sci, 284:2 (2024), 279  crossref
    2. B. Kh. Imomnazarov, Sh. Kh. Imomnazarov, M. M. Mamatkulov, B. B. Khudainazarov, “Fundamentalnoe reshenie dlya statsionarnogo uravneniya dvukhskorostnoi gidrodinamiki s ravnovesiem faz po davleniyu v dissipativnom priblizhenii”, Sib. zhurn. industr. matem., 25:3 (2022), 33–40  mathnet  crossref
    3. B. Kh. Imomnazarov, Sh. Kh. Imomnazarov, M. M. Mamatqulov, B. B. Khudainazarov, “The Fundamental Solution of the Steady-State Two-Velocity Hydrodynamics Equation with Phase Equilibrium Pressure in the Dissipative Approximation”, J. Appl. Ind. Math., 16:3 (2022), 403  crossref
    4. Kh. Kh. Imomnazarov, Sh. Kh. Imomnazarov, M. V. Urev, R. Kh. Bakhramov, “Reshenie odnoi pereopredelennoi statsionarnoi sistemy tipa Stoksa v v poluprostranstve”, Sib. zhurn. industr. matem., 24:4 (2021), 54–63  mathnet  crossref
    5. Kh. Kh. Imomnazarov, Sh. Kh. Imomnazarov, M. V. Urev, R. Kh. Bakhromov, “Solution of an Overdetermined Stationary Stokes-Type System in Half-Space”, J. Appl. Ind. Math., 15:4 (2021), 609  crossref
    6. Sarvar Kuyliev, Kholmatzhon Imomnazarov, Ilham Iskandarov, INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020, 2365, INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020, 2021, 070006  crossref
    7. M. V. Urev, Sh. Kh. Imomnazarov, “Klassicheskoe reshenie odnoi pereopredelennoi statsionarnoi sistemy, voznikayuschei v dvukhskorostnoi gidrodinamike”, Sib. elektron. matem. izv., 15 (2018), 1621–1629  mathnet  crossref
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