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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 5, Pages 1119–1136
DOI: https://doi.org/10.33048/smzh.2022.63.513 (Mi smj7718) 		 
The solvability of the Cauchy problem for a class of Sobolev-type equations in tempered distributions

A. L. Pavlovab

a Donetsk National University
b Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine
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DOI: https://doi.org/10.33048/smzh.2022.63.513
Abstract: We give sufficient conditions for the existence of a solution to the Cauchy problem for the equation $P_2(D_x)\partial_t^2{u} + P_0(D_x) u = 0$ in the space of tempered distributions.
Keywords: Cauchy problem, Sobolev-type equation, tempered distribution, multiplier.
Received: 18.08.2021
Revised: 18.08.2021
Accepted: 15.06.2022
English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 5, Pages 940–955
DOI: https://doi.org/10.1134/S0037446622050135
Document Type: Article
UDC: 517.955
MSC: 35R30
Language: Russian
Citation: A. L. Pavlov, “The solvability of the Cauchy problem for a class of Sobolev-type equations in tempered distributions”, Sibirsk. Mat. Zh., 63:5 (2022), 1119–1136; Siberian Math. J., 63:5 (2022), 940–955
Citation in format AMSBIB
\Bibitem{Pav22}
\by A.~L.~Pavlov
\paper The solvability of the Cauchy problem for a~class of Sobolev-type equations in tempered distributions
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 5
\pages 1119--1136
\mathnet{http://mi.mathnet.ru/smj7718}
\crossref{https://doi.org/10.33048/smzh.2022.63.513}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 5
\pages 940--955
\crossref{https://doi.org/10.1134/S0037446622050135}
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    		Сибирский математический журнал Siberian Mathematical Journal
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