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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 9 scientific papers (total in 9 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 (9)
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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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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