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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 1, Pages 115–126 (Mi zvmmf198)  
This article is cited in 11 scientific papers (total in 11 papers)

Inverse coefficient problem for a wave equation in a bounded domain

M. Yu. Kokurin, S. K. Paĭmerov

Mari State University, pl. Lenina 1, Ioshkar Ola, 424001, Russia
Full-text PDF (1209 kB) Citations (11)
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Abstract: The nonlinear inverse problem for a wave equation is investigated in a three-dimensional bounded domain subject to the Dirichlet boundary condition. Given a family of solutions to the equation defined on a closed surface within the original domain, it is required to reconstruct the coefficient determining the velocity of sound in the medium. The solutions used for this purpose correspond to the acoustic medium perturbations localized in the neighborhood of a certain closed surface. The inverse problem is reduced to a linear integral equation of the first kind, and the uniqueness of the solution to this equation is established. Numerical results are presented.
Key words: inverse problem, ill-posed problem, wave equation, linear integral equation of the first kind, uniqueness of a solution to an integral equation.
Received: 14.05.2007
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 1, Pages 109–120
DOI: https://doi.org/10.1007/s11470-008-1008-4
Bibliographic databases:
Document Type: Article
UDC: 519.633.9
Language: Russian
Citation: M. Yu. Kokurin, S. K. Paǐmerov, “Inverse coefficient problem for a wave equation in a bounded domain”, Zh. Vychisl. Mat. Mat. Fiz., 48:1 (2008), 115–126; Comput. Math. Math. Phys., 48:1 (2008), 109–120
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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