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Izv. Vyssh. Uchebn. Zaved. Mat., 2017, Number 3, Pages 37–50 (Mi ivm9215)  

This article is cited in 3 scientific papers (total in 3 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-31-00421_мол_а


Full text: PDF file (235 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:3, 31–43

Bibliographic databases:

UDC: 517.95
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

Citation in format AMSBIB
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\by K.~B.~Sabitov, V.~A.~Gushchina (Novikova)
\paper A.A.~Dezin's problem for inhomogeneous Lavrent'ev--Bitsadze equation
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2017
\issue 3
\pages 37--50
\mathnet{http://mi.mathnet.ru/ivm9215}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2017
\vol 61
\issue 3
\pages 31--43
\crossref{https://doi.org/10.3103/S1066369X17030045}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85014794913}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. A. Kirzhinov, “O reshenii analoga zadachi A. A. Dezina dlya uravneniya smeshannogo tipa vtorogo poryadka metodom funktsii Grina”, Vestnik KRAUNTs. Fiz.-mat. nauki, 2018, no. 3(23), 36–41  mathnet  crossref  elib
    2. Sabitov K.B., “Dezin Problem For An Equation of the Mixed Type With a Power-Law Degeneracy”, Differ. Equ., 55:10 (2019), 1384–1389  crossref  isi
    3. Zh. A. Balkizov, “On a boundary value problem for a third-order parabolic-hyperbolic type equation with a displacement boundary condition in its hyperbolicity domain”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 24:2 (2020), 211–225  mathnet  crossref
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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