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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 9, Pages 1492–1507
DOI: https://doi.org/10.31857/S0044466921090131 (Mi zvmmf11290) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Partial Differential Equations

On Lavrent'ev-type integral equations in coefficient inverse problems for wave equations

A. I. Kozlova, M. Yu. Kokurinb

a "Infosfera" Training Centern "Institute of Program Systems", 424000, Yoshkar-Ola, Mari Republic El, Russia
b Mari State University, 424000, Yoshkar-Ola, Mari Republic El, Russia
Citations (12)
DOI: https://doi.org/10.31857/S0044466921090131
Abstract: Coefficient inverse problems for second- and third-order equations with one or two unknown coefficients are investigated. The initial data are specified as the solution of an equation for a set of sounding sources averaged over time with power-law weights. It is shown that the original nonlinear inverse problems can be equivalently reduced to integral equations that are linear or nonlinear depending on the averaging method. It is proved that these equations have a unique solution determining the desired solution of the inverse problems. The results of a numerical experiment concerning the solution of a linear integral equation with a special kernel are presented.
Key words: hyperbolic equation, coefficient inverse problem, linear integral equation, biharmonic equation, uniqueness, numerical experiment.
Funding agency Grant number
Russian Science Foundation 20-11-20085
This work was supported by the Russian Science Foundation, project no. 20-11-20085.
Received: 01.01.2021
Revised: 01.01.2021
Accepted: 01.01.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 9, Pages 1470–1484
DOI: https://doi.org/10.1134/S0965542521090128
Bibliographic databases:
Document Type: Article
UDC: 519.635
Language: Russian
Citation: A. I. Kozlov, M. Yu. Kokurin, “On Lavrent'ev-type integral equations in coefficient inverse problems for wave equations”, Zh. Vychisl. Mat. Mat. Fiz., 61:9 (2021), 1492–1507; Comput. Math. Math. Phys., 61:9 (2021), 1470–1484
Citation in format AMSBIB
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\jour Zh. Vychisl. Mat. Mat. Fiz.
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Linking options:
  • https://www.mathnet.ru/eng/zvmmf11290
  • https://www.mathnet.ru/eng/zvmmf/v61/i9/p1492
    • This publication is cited in the following 12 articles:
    1. Alexander Goncharsky, Sergey Romanov, Sergey Seryozhnikov, Lecture Notes in Computer Science, 15406, Supercomputing, 2025, 111  crossref
    2. M. Yu. Kokurin, “Edinstvennost resheniya uravneniya M.M. Lavrenteva s istochnikami na okruzhnosti”, Izv. vuzov. Matem., 2025, no. 2, 53–60  mathnet  crossref
    3. Mikhail Yu. Kokurin, “M. M. Lavrentiev-type systems and reconstructing parameters of viscoelastic media”, Journal of Inverse and Ill-posed Problems, 2024  crossref
    4. Alexander V Goncharsky, Sergey Y Romanov, Sergey Y Seryozhnikov, “On mathematical problems of two-coefficient inverse problems of ultrasonic tomography”, Inverse Problems, 40:4 (2024), 045026  crossref
    5. M. M. Kokurin, V. V. Klyuchev, A. V. Gavrilova, “Uniqueness of a Solution to the Lavrent'ev Integral Equation in n-Dimensional Space”, Comput. Math. and Math. Phys., 64:3 (2024), 416  crossref
    6. M. M. Kokurin, V. V. Klyuchev, A. V. Gavrilova, “Uniqueness of a solution to the Lavrent'ev integral equation in n-dimensional space”, Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, 64:3 (2024), 443  crossref
    7. M. Yu. Kokurin, “Lavrent'ev-Type Equations and Systems in the Inverse Problem of Reconstructing Viscoelastic Medium Memory”, Comput. Math. and Math. Phys., 64:10 (2024), 2333  crossref
    8. M.Yu. Kokurin, “Completeness of products of homogeneous harmonic polynomials and uniqueness of the solution to an inverse wave sounding problem”, Journal of Mathematical Analysis and Applications, 517:1 (2023), 126584  crossref
    9. A. B. Bakushinsky, A. S. Leonov, “Multifrequency Inverse Problem of Scalar Acoustics: Remarks on Nonuniqueness and Solution Algorithm”, J Math Sci, 274:4 (2023), 460  crossref
    10. M. Yu. Kokurin, V. V. Klyuchev, “Usloviya edinstvennosti i chislennaya approksimatsiya resheniya integralnogo uravneniya M.M. Lavrenteva”, Sib. zhurn. vychisl. matem., 25:4 (2022), 441–458  mathnet  crossref
    11. A. B. Bakushinsky, A. S. Leonov, “Computing magnifier for refining the position and shape of three-dimensional objects in acoustic sensing”, Math. Models Comput. Simul., 14:6 (2022), 955–971  mathnet  crossref  crossref  mathscinet
    12. V. Klibanov M., Li J., Zhang W., “Linear Lavrent'Ev Integral Equation For the Numerical Solution of a Nonlinear Coefficient Inverse Problem”, SIAM J. Appl. Math., 81:5 (2021), 1954–1978  crossref  mathscinet  zmath  isi
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