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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2021, Volume 195, Pages 3–9
DOI: https://doi.org/10.36535/0233-6723-2021-195-3-9 (Mi into827) 		 
Asymptotic analysis of an elliptic boundary-value problem in a wedge

V. B. Vasilev (Vasilyev), Sh. Kutaiba, A. Z. Yaduta

National Research University "Belgorod State University"
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DOI: https://doi.org/10.36535/0233-6723-2021-195-3-9
Abstract: In this paper, we consider an elliptic pseudodifferential equation, whose symbol is independent of the spatial variable, in a wedge-shaped domain of a multidimensional space. Under a special wave factorization of the symbol, we construct in the Sobolev–Slobodetskii space the general solution of the equation, which depends on one arbitrary function. The equation is supplemented by an integral condition, which allows one to extract a unique solution. We examine the behavior of this solution in the case where the aperture of the wedge tends to zero.
Keywords: pseudodifferential operator, elliptic boundary-value problem, wave factorization of a symbol, general solution, asymptotic behavior, solvability condition.
Document Type: Article
UDC: 517.95, 517.983
MSC: 35S15, 45E05
Language: Russian
Citation: V. B. Vasilev (Vasilyev), Sh. Kutaiba, A. Z. Yaduta, “Asymptotic analysis of an elliptic boundary-value problem in a wedge”, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 195, VINITI, Moscow, 2021, 3–9
Citation in format AMSBIB
\Bibitem{VasKutYad21}
\by V.~B.~Vasilev~(Vasilyev), Sh.~Kutaiba, A.~Z.~Yaduta
\paper Asymptotic analysis of an elliptic boundary-value problem in a wedge
\inbook Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 195
\pages 3--9
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into827}
\crossref{https://doi.org/10.36535/0233-6723-2021-195-3-9}
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