Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 137, Pages 3–16 (Mi into202)  
Second boundary-value problem for the Lavrent'ev–Bitsadze equation in a rectangular domain with two degeneration lines

A. A. Gimaltdinova

Ufa State Petroleum Technological University
Full-text PDF (225 kB)
Abstract: For a mixed-type equation, we examine the second boundary-value problem and by using the spectral method prove the uniqueness and existence of solutions. The uniqueness criterion is proved based on the completeness property of the biorthogonal system of functions corresponding to the one-dimensional spectral problem. A solution of the problem is constructed as the sum of a biorthogonal series.
Keywords: equation of mixed type, biorthogonal system of functions, completeness, existence and uniqueness of solution.
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 236, Issue 6, Pages 579–593
DOI: https://doi.org/10.1007/s10958-018-4134-0
Bibliographic databases:
Document Type: Article
UDC: 517.956
MSC: 35M12
Language: Russian
Citation: A. A. Gimaltdinova, “Second boundary-value problem for the Lavrent'ev–Bitsadze equation in a rectangular domain with two degeneration lines”, Differential equations. Mathematical physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 137, VINITI, Moscow, 2017, 3–16; J. Math. Sci. (N. Y.), 236:6 (2019), 579–593
Citation in format AMSBIB
\Bibitem{Gim17}
\by A.~A.~Gimaltdinova
\paper Second boundary-value problem for the Lavrent'ev--Bitsadze equation in a rectangular domain with two degeneration lines
\inbook Differential equations. Mathematical physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 137
\pages 3--16
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into202}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801257}
\zmath{https://zbmath.org/?q=an:1414.35131}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 236
\issue 6
\pages 579--593
\crossref{https://doi.org/10.1007/s10958-018-4134-0}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85059487867}
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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