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Izvestiya: Mathematics, 2018, Volume 82, Issue 2, Pages 318–350
DOI: https://doi.org/10.1070/IM8596 (Mi im8596) 		 
This article is cited in 16 scientific papers (total in 16 papers)

The first boundary-value problem for an equation of mixed type with a singular coefficient

K. B. Sabitovab, R. M. Safinac

a Institute of Applied Research, Sterlitamak
b Sterlitamak Branch of Bashkir State University
c Volga Region State Academy of Physical Culture, Sport and Tourism
English version PDF (488 kB) Citations (16) Russian version article
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DOI: https://doi.org/10.1070/IM8596
Abstract: We study the first boundary-value problem in a rectangle for an equation of mixed type with a singular coefficient. We establish a criterion for the uniqueness of solutions and construct the solution as the sum of a series in the system of eigenfunctions of a one-dimensional eigenvalue problem. Justifying the uniform convergence of the series encounters a problem of small denominators. To deal with this we obtain bounds for the separation of the small denominators from zero along with the corresponding asymptotic results. These bounds enable us to justify the convergence of the series in the class of regular solutions of the equation.
Keywords: equation of mixed type, singular coefficient, Dirichlet problem, Keldysh problem, survey, uniqueness, orthogonal series, small denominators, bounds, existence, stability.
Funding agency Grant number
Russian Foundation for Basic Research 16-31-50008 мол\_нр
17-41-020516 р\_а
This paper was written with the support of the Russian Foundation for Basic Research (grant no.~16-31-50008~mol\_nr), Russian Foundation for Basic Research and Republic Bashkortostan (grant no.~17-41-020516~r\_a).
Received: 02.09.2016
Bibliographic databases:
Document Type: Article
UDC: 517.95
MSC: 35M12
Language: English
Original paper language: Russian
Citation: K. B. Sabitov, R. M. Safina, “The first boundary-value problem for an equation of mixed type with a singular coefficient”, Izv. Math., 82:2 (2018), 318–350
Citation in format AMSBIB
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\by K.~B.~Sabitov, R.~M.~Safina
\paper The first boundary-value problem for an equation of mixed type with a~singular coefficient
\jour Izv. Math.
\yr 2018
\vol 82
\issue 2
\pages 318--350
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\crossref{https://doi.org/10.1070/IM8596}
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  • https://doi.org/10.1070/IM8596
  • https://www.mathnet.ru/eng/im/v82/i2/p79
    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:690
    Russian version PDF:134
    English version PDF:30
    References:93
    First page:72
     
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