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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, Number 3, Pages 37–50
(Mi ivm9215)
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This article is cited in 7 scientific papers (total in 7 papers)
A.A. Dezin's problem for inhomogeneous Lavrent'ev–Bitsadze equation
K. B. Sabitov, V. A. Gushchina (Novikova) Samara State University of Social Sciences and Education,
65/67 Gor’kogo str., Samara, 443090 Russia
Abstract:
We establish a criterion for the uniqueness of a solution to nonlocal Dezin's problem for an equation of mixed elliptic-hyperbolic type. The solution is constructed in the form of a sum of a series in eigenfunctions of the corresponding one-dimensional spectral problem. In substantiation of the convergence of series a problem of small denominators arizes. Under certain specified conditions with respect to given pagameters and functions we prove the convergence of constructed series in a class of regular solutions.
Keywords:
inhomogeneous equation of mixed type, nonlocal problem, inhomogeneous boundary condition, spectral method, uniqueness, existence, series.
Received: 14.09.2015
Citation:
K. B. Sabitov, V. A. Gushchina (Novikova), “A.A. Dezin's problem for inhomogeneous Lavrent'ev–Bitsadze equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 3, 37–50; Russian Math. (Iz. VUZ), 61:3 (2017), 31–43
Linking options:
https://www.mathnet.ru/eng/ivm9215 https://www.mathnet.ru/eng/ivm/y2017/i3/p37
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