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Vestnik KRAUNC. Fiziko-Matematicheskie Nauki, 2022, Volume 39, Number 2, Pages 7–19
DOI: https://doi.org/10.26117/2079-6641-2022-39-2-7-19 (Mi vkam534) 		 
MATHEMATICS

35M12Boundary value problem for a mixed-type equation with a higher order elliptic operator

R. R. Ashurova, M. B. Murzambetovab

a Institute of Mathematics named after V. I. Romanovskiy, Academy of Sciences of the Republic of Uzbekistan
b Nukus state pedagogical institute named after Ajiniyaz
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DOI: https://doi.org/10.26117/2079-6641-2022-39-2-7-19
Abstract: In this paper, we consider a boundary value problem for a mixed-type equation with a positive,formally self-adjoint, high order elliptic operator. The results of the work were obtained usingthe Fourier method. Theorems on the existence and uniqueness of the classical solution of theproblem are proved. In this case, the positivity of elliptic operator turned out to be essential.At the end of the paper, a mixed-type equation with a non-negative elliptic operator is considered,and it is shown that the solution of the corresponding problem is not unique.
Keywords: boundary value problem, method Fourier, elliptic operator.
Bibliographic databases:
Document Type: Article
UDC: 517.956
MSC: 35M12
Language: Russian
Citation: R. R. Ashurov, M. B. Murzambetova, “35M12Boundary value problem for a mixed-type equation with a higher order elliptic operator”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 39:2 (2022), 7–19
Citation in format AMSBIB
\Bibitem{AshMur22}
\by R.~R.~Ashurov, M.~B.~Murzambetova
\paper 35M12Boundary value problem for a mixed-type equation with a higher order elliptic operator
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
\yr 2022
\vol 39
\issue 2
\pages 7--19
\mathnet{http://mi.mathnet.ru/vkam534}
\crossref{https://doi.org/10.26117/2079-6641-2022-39-2-7-19}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4484488}
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