D. K. Durdiev, A. A. Rakhmonov, “Inverse problem for a system of integro-differential equations for SH waves in a visco-elastic porous medium: Global solvability”, TMF, 195:3 (2018), 491–506; Theoret. and Math. Phys., 195:3 (2018), 923

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Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 195, Number 3, Pages 491–506
DOI: https://doi.org/10.4213/tmf9480 (Mi tmf9480)

This article is cited in 47 scientific papers (total in 47 papers)

Inverse problem for a system of integro-differential equations for SH waves in a visco-elastic porous medium: Global solvability

D. K. Durdiev, A. A. Rakhmonov

Bukhara State University, Bukhara, Uzbekistan

Full-text PDF (442 kB) Citations (47)

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DOI: https://doi.org/10.4213/tmf9480

Abstract: We consider a system of hyperbolic integro-differential equations for SH waves in a visco-elastic porous medium. The inverse problem is to recover a kernel (memory) in the integral term of this system. We reduce this problem to solving a system of integral equations for the unknown functions. We apply the principle of contraction mappings to this system in the space of continuous functions with a weight norm. We prove the global unique solvability of the inverse problem and obtain a stability estimate of a solution of the inverse problem.

Keywords: integro-differential equation, inverse problem, Dirac delta function, kernel, hyperbolic equation, Lame coefficient, global solvability, weight function.

Received: 06.10.2017

English version:
Theoretical and Mathematical Physics, 2018, Volume 195, Issue 3, Pages 923–937
DOI: https://doi.org/10.1134/S0040577918060090

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: D. K. Durdiev, A. A. Rakhmonov, “Inverse problem for a system of integro-differential equations for SH waves in a visco-elastic porous medium: Global solvability”, TMF, 195:3 (2018), 491–506; Theoret. and Math. Phys., 195:3 (2018), 923–937

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This publication is cited in the following 47 articles:

Haniye Dehestani, Yadollah Ordokhani, Mohsen Razzaghi, “Ritz-least squares support vector regression technique for the system of fractional Fredholm-Volterra integro-differential equations”, J. Appl. Math. Comput., 2025
Jurabek Safarov, Askar Rakhmonov, Maftunakhon Safarova, 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, 040006
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
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, 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
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
Jonibek Jumaev, Zavqiddin Bozorov, Istam Shadmanov, Dilshod Atoev, 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, 040004
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
M. R. Tomaev, Zh. D. Totieva, “An inverse two-dimensional problem for determining two unknowns in equation of memory type for a weakly horizontally inhomogeneous medium”, Vladikavk. matem. zhurn., 26:3 (2024), 112–134
A. A. Boltayev, D. K. Durdiev, A. A. Rahmonov, “Kernel determination problem in the third order 1D Moore–Gibson–Thompson equation with memory”, Vladikavk. matem. zhurn., 26:4 (2024), 55–65
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, Kh. Kh. Turdiev, “Zadacha opredeleniya yader v sisteme integro-differentsialnykh uravnenii akustiki”, Dalnevost. matem. zhurn., 23:2 (2023), 190–210
D. I. Akramova, “Obratnaya koeffitsientnaya zadacha dlya drobno-diffuzionnogo uravneniya s operatorom Besselya”, Izv. vuzov. Matem., 2023, no. 9, 45–57
D. K. Durdiev, A. A. Boltaev, A. A. Rakhmonov, “Zadacha opredeleniya yadra tipa svertki v uravnenii Mura–Gibsona–Tomsona tretego poryadka”, Izv. vuzov. Matem., 2023, no. 12, 3–16
Ufa Math. J., 15:2 (2023), 119–134
M. Tomaev, Zh. Totieva, “Numerical solution of a two-dimensional problem of determining the propagation velocity of seismic waves in inhomogeneous medium of memory type”, Russian Journal of Earth Sciences, 23:4 (2023), 1–16
M. A. Sultanov, D. Durdiev, A. Rahmonov, R. Turebekov, Y. Nurlanuly, “Source identification problems for time-fractional diffusion equation”, Sixth international conference of mathematical sciences (ICMS 2022), AIP Conf. Proc., 2879, no. 1, 2023, 040002
D. K. Durdiev, J. J. Jumaev, “One-dimensional inverse problems of determining the kernel of the integro-differential heat equation in a bounded domain”, Nonautonomous Dynamical Systems, 10:1 (2023), 20220163
D. K. Durdiev, A. A. Boltaev, A. A. Rahmonov, “Convolution Kernel Determination Problem in the Third Order Moore–Gibson–Thompson Equation”, Russ Math., 67:12 (2023), 1
D. I. Akramova, “Inverse Coefficient Problem for a Fractional-Diffusion Equation with a Bessel Operator”, Russ Math., 67:9 (2023), 39

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

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