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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 6, Pages 61–72 (Mi ivm9124)  

This article is cited in 5 scientific papers (total in 5 papers)

Nonlocal A. A. Dezin's problem for Lavrent'ev–Bitsadze equation

K. B. Sabitov, V. A. Novikova

Volga Region State Socially-Humanitarian Academy, 65/67 Gorky str., Samara, 443099 Russia

Abstract: For mixed type equation $u_{xx}+(\operatorname{sgn}y)u_{yy}=0$ in the rectangular domain by the method of spectral analysis we establish a criterion of uniqueness of the solution to a problem with the periodicity conditions on the variable $x$, nonlocal condition and the boundary condition. The solution is constructed as the sum of a series in eigenfunctions corresponding to one-dimensional spectral problem. In the substantiation of convergence of series the problem of small denominators arises. Under certain conditions on the parameters and the given functions we prove uniform convergence of the constructed series and stability of the solution from the set of these functions.

Keywords: mixed type equation, non-local problem, criterion of uniqueness, small denominators, stability.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:6, 52–62

Bibliographic databases:

UDC: 517.957
Received: 29.10.2014

Citation: K. B. Sabitov, V. A. Novikova, “Nonlocal A. A. Dezin's problem for Lavrent'ev–Bitsadze equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 6, 61–72; Russian Math. (Iz. VUZ), 60:6 (2016), 52–62

Citation in format AMSBIB
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\by K.~B.~Sabitov, V.~A.~Novikova
\paper Nonlocal A.\,A.~Dezin's problem for Lavrent'ev--Bitsadze equation
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
\issue 6
\pages 61--72
\mathnet{http://mi.mathnet.ru/ivm9124}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2016
\vol 60
\issue 6
\pages 52--62
\crossref{https://doi.org/10.3103/S1066369X16060074}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Guschina, “Nelokalnaya zadacha A. A. Dezina dlya uravneniya smeshannogo elliptiko-giperbolicheskogo tipa”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:1 (2016), 22–32  mathnet  crossref  zmath  elib
    2. V. A. Guschina, “Kriterii edinstvennosti resheniya zadachi Dezina dlya uravneniya smeshannogo tipa so stepennym vyrozhdeniem”, Vestn. SamU. Estestvennonauchn. ser., 2016, no. 3-4, 24–31  mathnet  elib
    3. K. B. Sabitov, V. A. Gushchina (Novikova), “A.A. Dezin's problem for inhomogeneous Lavrent'ev–Bitsadze equation”, Russian Math. (Iz. VUZ), 61:3 (2017), 31–43  mathnet  crossref  isi
    4. 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
    5. 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
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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