Abstract:
In this paper, we study a Dirichlet type problem for a Lavrentiev–Bitsadze type equation of high order type in a rectangular domain. The necessary and sufficient conditions for the uniqueness of the problem solution are obtained by using the spectral method. The solution is constructed in the form of a series of eigenfunctions. When substantiating the convergence of a series, the problem of «small» denominators arises. Sufficient conditions are obtained for the separability of the «small» denominator from zero.
\Bibitem{Irg20}
\by B.~Yu.~Irgashev
\paper On a boundary value problem for a high order mixed type equation
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 899--912
\mathnet{http://mi.mathnet.ru/semr1260}
\crossref{https://doi.org/10.33048/semi.2020.17.066}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000548270300001}
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This publication is cited in the following 3 articles:
A. K. Urinov, M. S. Azizov, “Initial-Boundary Value Problem for a Degenerate High Even-Order Partial Differential Equation with the Bessel Operator”, Lobachevskii J Math, 45:2 (2024), 864
A. K. Urinov, D. A. Usmonov, “Ob odnoi zadache dlya uravneniya smeshannogo tipa chetvertogo poryadka, vyrozhdayuschegosya vnutri i na granitse oblasti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 33:2 (2023), 312–328
A. K. Urinov, M. S. Azizov, “O razreshimosti nelokalnykh nachalno-granichnykh zadach dlya odnogo differentsialnogo uravneniya v chastnykh proizvodnykh vysokogo chetnogo poryadka”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:2 (2022), 240–255
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