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Sibirskii Matematicheskii Zhurnal, 2023, Volume 64, Number 5, Pages 895–911
DOI: https://doi.org/10.33048/smzh.2023.64.502 (Mi smj7804) 		 
On well-posedness of the Cauchy problem for pseudohyperbolic equations in weighted Sobolev spaces

L. N. Bondar'ab, G. V. Demidenkoab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
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DOI: https://doi.org/10.33048/smzh.2023.64.502
Abstract: We consider a class of strictly pseudohyperbolic equations and establish some solvability conditions of the Cauchy problem in the class of weighted Sobolev spaces. We also prove the uniqueness of solutions and obtain some estimates.
Keywords: equations that are not solved with respect to the higher-order derivative, pseudohyperbolic equations, energy estimate.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0008
Received: 04.05.2023
Revised: 04.05.2023
Accepted: 16.05.2023
Document Type: Article
UDC: 517.955
MSC: 35R30
Language: Russian
Citation: L. N. Bondar', G. V. Demidenko, “On well-posedness of the Cauchy problem for pseudohyperbolic equations in weighted Sobolev spaces”, Sibirsk. Mat. Zh., 64:5 (2023), 895–911
Citation in format AMSBIB
\Bibitem{BonDem23}
\by L.~N.~Bondar', G.~V.~Demidenko
\paper On well-posedness of the Cauchy problem for pseudohyperbolic equations in weighted Sobolev spaces
\jour Sibirsk. Mat. Zh.
\yr 2023
\vol 64
\issue 5
\pages 895--911
\mathnet{http://mi.mathnet.ru/smj7804}
\crossref{https://doi.org/10.33048/smzh.2023.64.502}
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