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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
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.
Received: 01.01.2021 Revised: 01.01.2021 Accepted: 01.01.2021
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
Linking options:
https://www.mathnet.ru/eng/zvmmf11290 https://www.mathnet.ru/eng/zvmmf/v61/i9/p1492
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