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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 9, Pages 1536–1544
DOI: https://doi.org/10.31857/S0044466921090052 (Mi zvmmf11293) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Mathematical physics

Solution of inverse problems for wave equation with a nonlinear coefficient

A. V. Bayev

Lomonosov Moscow State University, 119991, Moscow, Russia
Citations (1)
DOI: https://doi.org/10.31857/S0044466921090052
Abstract: Two hyperbolic equations with a nonlinear coefficient multiplying the highest derivative are considered. The coefficient determines the velocity of nonlinear waves and characterizes the scattering properties of the medium. For stationary traveling-wave solutions, inverse problems are set up consisting of determining a nonlinear coefficient from the dependence of the period on the amplitude of the stationary oscillations. Nonlinear integral functional equations of the inverse problems are obtained and studied, and sufficient conditions for the existence and uniqueness of solutions to the inverse problems are steady-state. Evolution-type algorithms for solving functional equations are proposed. Solutions of test inverse problems are presented.
Key words: wave equation, stationary solution, integral functional equation, blow-up mode.
Funding agency Grant number
Moscow Center of Fundamental and Applied Mathematics 075-15-2019-1621
This paper was published with the financial support of the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics under agreement no. 075-15-2019-1621.
Received: 23.02.2021
Revised: 23.02.2021
Accepted: 23.02.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 9, Pages 1511–1520
DOI: https://doi.org/10.1134/S0965542521090049
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
Citation: A. V. Bayev, “Solution of inverse problems for wave equation with a nonlinear coefficient”, Zh. Vychisl. Mat. Mat. Fiz., 61:9 (2021), 1536–1544; Comput. Math. Math. Phys., 61:9 (2021), 1511–1520
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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