D. K. Durdiev, K. K. Turdiev, “The problem of finding the kernels in the system of integro-differential Maxwell's equations”, Sib. Zh. Ind. Mat., 24:2 (2021), 38–61; J. Appl. Industr. Math., 15:2 (2021), 190

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Sibirskii Zhurnal Industrial'noi Matematiki, 2021, Volume 24, Number 2, Pages 38–61
DOI: https://doi.org/10.33048/SIBJIM.2021.24.203 (Mi sjim1128)

This article is cited in 18 scientific papers (total in 18 papers)

The problem of finding the kernels in the system of integro-differential Maxwell's equations

D. K. Durdiev^ab, K. K. Turdiev^b

^a The Institute of Mathematics named after V.I. Romanovskiy at the Academy of Sciences of the Republic of Uzbekistan, ul. M. Ikbal 11, Bukhara 200117, Uzbekistan
^b Bukhara State University, ul. M. Ikbal 11, Bukhara 200117, Uzbekistan

Full-text PDF (648 kB) Citations (18)

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DOI: https://doi.org/10.33048/SIBJIM.2021.24.203

Abstract: We pose the direct and inverse problem of finding the electromagnetic field and the diagonal memory matrix for the reduced canonical system of integro-differential Maxwell's equations. The problems are replaced by a closed system of Volterra-type integral equations of the second kind with respect to the Fourier transform in the variables

$x_1$ and

$x_2$ of the solution to the direct problem and the unknowns of the inverse problem. To this system, we then apply the method of contraction mapping in the space of continuous functions with a weighted norm. Thus, we prove the global existence and uniqueness theorems for solutions to the posed problems.

Keywords: hyperbolic system, system of Maxwell's equations, integral equation, contraction mapping principle.

Received: 13.01.2021
Revised: 11.02.2021
Accepted: 15.04.2021

English version:
Journal of Applied and Industrial Mathematics, 2021, Volume 15, Issue 2, Pages 190–211
DOI: https://doi.org/10.1134/S1990478921020022

Bibliographic databases:

Document Type: Article

UDC: 517.968.72

Language: Russian

Citation: D. K. Durdiev, K. K. Turdiev, “The problem of finding the kernels in the system of integro-differential Maxwell's equations”, Sib. Zh. Ind. Mat., 24:2 (2021), 38–61; J. Appl. Industr. Math., 15:2 (2021), 190–211

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sjim1128

https://www.mathnet.ru/eng/sjim/v24/i2/p38

This publication is cited in the following 18 articles:

D. K. Durdiev, T. R. Suyarov, Kh. Kh. Turdiev, “Obratnaya koeffitsientnaya zadacha dlya drobnogo telegrafnogo uravneniya s sootvetstvuyuschei drobnoi proizvodnoi po vremeni”, Izv. vuzov. Matem., 2025, no. 2, 39–52
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
Askar Rahmonov, Durdimurod Durdiev, Dilshoda Akramova, 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, 040012
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
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
D. K. Durdiev, H. H. Turdiev, “Determining of a Space Dependent Coefficient of Fractional Diffusion Equation with the Generalized Riemann–Liouville Time Derivative”, Lobachevskii J Math, 45:2 (2024), 648
D. K. Durdiev, J.J. Jumaev, H. H. Turdiev, “INVERSE PROBLEM FOR DETERMINING TIME DEPENDENT COEFFICIENT AND SOURCE FUNCTIONS IN A TIME-FRACTIONAL DIFFUSION EQUATION”, J Math Sci, 2024
H. H. Turdiev, “Solvability Cauchy Problem for Time-Space Fractional Diffusion-Wave Equation with Variable Coefficient”, Lobachevskii J Math, 45:10 (2024), 5281
D. K. Durdiev, Kh. Kh. Turdiev, “Zadacha opredeleniya yader v sisteme integro-differentsialnykh uravnenii akustiki”, Dalnevost. matem. zhurn., 23:2 (2023), 190–210
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
Kh. Kh. Turdiev, “Obratnye koeffitsientnye zadachi dlya vremenno-drobnogo volnovogo uravneniya s obobschennoi proizvodnoi Rimana–Liuvillya po vremeni”, Izv. vuzov. Matem., 2023, no. 10, 46–59
D. K. Durdiev, Z. R. Bozorov, A. A. Boltayev, “Inverse problem for the system of viscoelasticity in anisotropic media with tetragonal form of elasticity modulus”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 33:4 (2023), 581–600
Durdimurod Durdiev, Halim Turdiev, “Inverse Coefficient Problem for Fractional Wave Equation with the Generalized Riemann–Liouville Time Derivative”, Indian J Pure Appl Math, 2023
U. D. Durdiev, “Inverse Source Problem for the Equation of Forced Vibrations of a Beam”, Russ Math., 67:8 (2023), 7
H. H. Turdiev, “Inverse Coefficient Problems for a Time-Fractional Wave Equation with the Generalized Riemann–Liouville Time Derivative”, Russ Math., 67:10 (2023), 14
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

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

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