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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2022, Volume 7, Issue 1, Pages 30–42
DOI: https://doi.org/10.47475/2500-0101-2022-17103 (Mi chfmj269) 		 
Mathematics

Investigation of the influence of parameters on the correctness of the conjugation problem for the Boussinesq — Löve

A. I. Kozhanova, N. N. Shadrinabc

a S.L. Sobolev Institute of Mathematics of Siberian Branch of RAS, Novosibirsk, Russia
b Bauman Moscow State Technical University, Moscow, Russia
c MIREA — Russian Technological University, Moscow, Russia
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DOI: https://doi.org/10.47475/2500-0101-2022-17103
Abstract: The aim of this work is to study the solvability of boundary value problems for differential equations $u_{tt}-\Delta u_{tt}+\lambda\Delta u=\mu u+f(x,t)$ with the Dirichlet boundary conditions, as well as with some matching conditions on the line $t=0$. For the problems under study, the properties of existence, uniqueness and non-uniqueness of a regular solution are established (i.e. solutions having all generalized derivatives by S.L. Sobolev included in the equation).
Keywords: Boussinesq — Löve equation, boundary value problem, conjugation conditions, regular solution, existence of solution, uniqueness of solution, influence of parameters.
Funding agency Grant number
Russian Foundation for Basic Research 20-41-740004
The research was carried out with the financial support of the Russian Foundation for Basic Research and the Chelyabinsk Region within the framework of the scientific project No. 20-41-740004.
Received: 13.11.2021
Revised: 10.12.2021
Document Type: Article
UDC: 517.95
Language: Russian
Citation: A. I. Kozhanov, N. N. Shadrina, “Investigation of the influence of parameters on the correctness of the conjugation problem for the Boussinesq — Löve”, Chelyab. Fiz.-Mat. Zh., 7:1 (2022), 30–42
Citation in format AMSBIB
\Bibitem{KozSha22}
\by A.~I.~Kozhanov, N.~N.~Shadrina
\paper Investigation of the influence of parameters on the correctness of the conjugation problem for the Boussinesq~--- L\"ove
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2022
\vol 7
\issue 1
\pages 30--42
\mathnet{http://mi.mathnet.ru/chfmj269}
\crossref{https://doi.org/10.47475/2500-0101-2022-17103}
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