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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) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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
This work was carried out within the framework of the state task for Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, project no. 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}
\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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