D. K. Durdiev, A. A. Rahmonov, “The problem of determining the 2D-kernel in a system of integro-differential equations of a viscoelastic porous medium”, Sib. Zh. Ind. Mat., 23:2 (2020), 63–80; J. Appl. Industr. Math., 14:2 (2020), 281

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Sibirskii Zhurnal Industrial'noi Matematiki, 2020, Volume 23, Number 2, Pages 63–80
DOI: https://doi.org/10.33048/SIBJIM.2020.23.205 (Mi sjim1088)

This article is cited in 31 scientific papers (total in 31 papers)

The problem of determining the 2D-kernel in a system of integro-differential equations of a viscoelastic porous medium

D. K. Durdiev, A. A. Rahmonov

Bukhara State University, ul. M.Ikbol 11, Bukhara 200117, Uzbekistan

Full-text PDF (622 kB) Citations (31)

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DOI: https://doi.org/10.33048/SIBJIM.2020.23.205

Abstract: Under consideration is the system of integro-differential equations of viscoelastic porous medium. The direct problem is to define the

$y$ -component of the displacement vectors of the elastic porous body and the liquid from the initial boundary value problem for these equations. We assume that the kernel of the integral term of the first equation depends on time and one of the spatial variables. To determine the kernel, some additional condition is given on the solution of the direct problem for

$z=0$ . The inverse problem is replaced by an equivalent system of integro-differential equations for the unknown functions. We apply the method of scales of the Banach spaces of analytic functions. The local solvability of the inverse problem is proved in the class of the functions analytic in

$x$ and continuous in

$t$ .

Keywords: inverse problem, kernel, Dirac delta function, integro-differential equation, analytic function.

Received: 04.02.2020
Revised: 23.03.2020
Accepted: 09.04.2020

English version:
Journal of Applied and Industrial Mathematics, 2020, Volume 14, Issue 2, Pages 281–295
DOI: https://doi.org/10.1134/S1990478920020076

Bibliographic databases:

Document Type: Article

UDC: 517.958

Language: Russian

Citation: D. K. Durdiev, A. A. Rahmonov, “The problem of determining the 2D-kernel in a system of integro-differential equations of a viscoelastic porous medium”, Sib. Zh. Ind. Mat., 23:2 (2020), 63–80; J. Appl. Industr. Math., 14:2 (2020), 281–295

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sjim1088

https://www.mathnet.ru/eng/sjim/v23/i2/p63

This publication is cited in the following 31 articles:

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Durdimurod Durdiev, Javlon Nuriddinov, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 3045, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 2024, 040013
Jonibek Jumaev, Durdimurod Durdiev, Shakhnoza Ibragimova, Bekhzod Zaripov, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 3045, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 2024, 040011
Durdimurod Durdiev, Javlon Nuriddinov, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 3045, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 2024, 040014
Zavqiddin Bozorov, Halim Turdiev, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 3045, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 2024, 040010
Durdimurod Durdiev, Halim Turdiev, Asliddin Boltaev, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 3045, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 2024, 040015
Zhanna D. Totieva, “A global in time existence and uniqueness result of a multidimensional inverse problem”, Applicable Analysis, 103:4 (2024), 701
Zh. Sh. Safarov, “Obratnaya zadacha dlya integro-differentsialnogo uravneniya giperbolicheskogo tipa s dopolnitelnoi informatsiei spetsialnogo vida v ogranichennoi oblasti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 28:1 (2024), 29–44
J. Sh. Safarov, D. K. Durdiev, A. A. Rakhmonov, “Inverse problem for a hyperbolic integro-differential equation in a bounded domain”, Siberian Adv. Math., 34:2 (2024), 154–166
J. Sh. Safarov, U. N. Kalandarov, M. J. Safarova, “Inverse Problem of Determining a Kernel of the Viscoelasticity Equation with Distributed Data in a Limited Domain”, Lobachevskii J Math, 45:7 (2024), 3380
D. K. Durdiev, A. A. Boltaev, “Zadacha opredeleniya yader v dvumernoi sisteme uravnenii vyazkouprugosti”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 43 (2023), 31–47
D. K. Durdiev, J. Sh. Safarov, J. Sh. Safarov, “Inverse Problem for an Integrodifferential Equation of the Hyperbolic Type protect in a Rectangular Domain”, Math. Notes, 114:2 (2023), 199–211
U. D. Durdiev, Z. R. Bozorov, “Nonlocal inverse problem for determining the unknown coefficient in the beam vibration equation”, J. Appl. Industr. Math., 17:2 (2023), 281–290
D. K. Durdiev, Kh. Kh. Turdiev, “Zadacha opredeleniya yader v sisteme integro-differentsialnykh uravnenii akustiki”, Dalnevost. matem. zhurn., 23:2 (2023), 190–210
Murat A. Sultanov, Durdimurod Durdiev, Askar Rahmonov, Rauan Turebekov, Yerkebulan Nurlanuly, SIXTH INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2022), 2879, SIXTH INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2022), 2023, 040002
U. D. Durdiev, “Inverse Problem of Determining the Unknown Coefficient in the Beam Vibration Equation in an Infinite Domain”, Diff Equat, 59:4 (2023), 462
U. D. Durdiev, “A Time-Nonlocal Inverse Problem for the Beam Vibration Equation with an Integral Condition”, Diff Equat, 59:3 (2023), 359
D. K. Durdiev, J. J. Jumaev, D. D. Atoev, “Inverse problem on determining two kernels in integro-differential equation of heat flow”, Ufa Math. J., 15:2 (2023), 119–134
Durdiev D.K., Zhumaev Zh.Zh., “Memory Kernel Reconstruction Problems in the Integro-Differential Equation of Rigid Heat Conductor”, Math. Meth. Appl. Sci., 45:14 (2022), 8374–8388
D. K. Durdiev, Zh. Sh. Safarov, “Zadacha ob opredelenii dvumernogo yadra uravneniya vyazkouprugosti so slabo gorizontalnoi neodnorodnostyu”, Sib. zhurn. industr. matem., 25:1 (2022), 14–38

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

Сибирский журнал индустриальной математики

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