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Sibirskii Zhurnal Industrial'noi Matematiki, 2023, Volume 26, Number 2, Pages 113–129
DOI: https://doi.org/10.33048/SIBJIM.2023.26.210 (Mi sjim1235) 		 
The problem of determining the coefficient for power gradient nonlinearity in semilinear wave equation

V. G. Romanova, T.V. Buguevaba

a Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia
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DOI: https://doi.org/10.33048/SIBJIM.2023.26.210
Abstract: An one-dimensional inverse problem of determining the coefficient for power gradient nonlinearity in a semilinear wave equation is considered. The existence and uniqueness theorems of the solution of a direct problem are proved. For the inverse problem the local existence theorem is stated and a stability estimate of the solution is found.
Keywords: semilinear wave equation, direct problem, inverse problem, power gradient nonlinearity, existence, stability, uniqueness. .
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0009
Received: 12.12.2022
Revised: 14.12.2022
Accepted: 12.01.2023
English version:
Journal of Applied and Industrial Mathematics, 2023, Volume 17, Issue 2, Pages 370–384
DOI: https://doi.org/10.1134/S1990478923020151
Document Type: Article
UDC: 517.956
Language: Russian
Citation: V. G. Romanov, T.V. Bugueva, “The problem of determining the coefficient for power gradient nonlinearity in semilinear wave equation”, Sib. Zh. Ind. Mat., 26:2 (2023), 113–129; J. Appl. Industr. Math., 17:2 (2023), 370–384
Citation in format AMSBIB
\Bibitem{RomBug23}
\by V.~G.~Romanov, T.V.~Bugueva
\paper The problem of determining the coefficient for power gradient nonlinearity in semilinear wave equation
\jour Sib. Zh. Ind. Mat.
\yr 2023
\vol 26
\issue 2
\pages 113--129
\mathnet{http://mi.mathnet.ru/sjim1235}
\crossref{https://doi.org/10.33048/SIBJIM.2023.26.210}
\transl
\jour J. Appl. Industr. Math.
\yr 2023
\vol 17
\issue 2
\pages 370--384
\crossref{https://doi.org/10.1134/S1990478923020151}
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    		Сибирский журнал индустриальной математики
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