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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2019, Volume 59, Number 4, Pages 587–596
DOI: https://doi.org/10.1134/S0044466919040021 (Mi zvmmf10877) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Existence of a solution of the inverse coefficient problem for a quasilinear hyperbolic equation

A. M. Denisov

Lomonosov Moscow State University, Moscow, 119992 Russia
Citations (7)
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DOI: https://doi.org/10.1134/S0044466919040021
Abstract: A problem with data on the characteristics for a quasilinear hyperbolic equation is considered. An inverse problem consisting in determining the unknown coefficient of the equation, depending on its solution, is formulated. As additional information for the inverse problem, the values of the solution of the problem with the data on the characteristics at a fixed value of one of the independent variables are specified. The existence theorem for the inverse problem is proved. The proof is based on deriving a nonlinear operator equation for the unknown coefficient and the proof of its solvability.
Key words: quasilinear hyperbolic equation, problem with data on characteristics, inverse problem, existence theorem, nonlinear operator equation.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00525_а
This work was supported in part by the Russian Foundation for Basic Research, project no. 17-01-00525.
Received: 10.10.2018
Revised: 14.11.2018
Accepted: 14.11.2018
English version:
Computational Mathematics and Mathematical Physics, 2019, Volume 59, Issue 4, Pages 550–558
DOI: https://doi.org/10.1134/S096554251904002X
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: A. M. Denisov, “Existence of a solution of the inverse coefficient problem for a quasilinear hyperbolic equation”, Zh. Vychisl. Mat. Mat. Fiz., 59:4 (2019), 587–596; Comput. Math. Math. Phys., 59:4 (2019), 550–558
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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