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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, Number 9, Pages 42–58 (Mi ivm9396)  
This article is cited in 6 scientific papers (total in 6 papers)

Dirichlet problem for Lavrent'ev–Bitsadze equation with loaded summands

Yu. K. Sabitovaab

a Sterlitamak Branch of Bashkir State University, 49 Lenin Ave., Sterlitamak, 453100 Russia
b Institute of Strategic Studies of Bashkortostan Republic, Sterlitamak Branch
Full-text PDF (254 kB) Citations (6)
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Abstract: We study the first boundary-value problem for loaded equation of elliptic-hyperbolic type in rectangular domain. We establish a criterion of uniqueness. A solution to the problem is constructed in the form of the sum of a series. In substantiation of existence of a solution to a problem small denominators appear. We obtain the estimates about a separation from zero of denominators with the corresponding asymptotics. They allow to prove existence of a solution in a class of regular solutions.
Keywords: loaded equation of mixed type, Dirichlet's problem, criterion of uniqueness, existence, series, small denominator, estimate, uniform convergence.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-97003_р_поволжье_а
Received: 02.05.2017
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2018, Volume 62, Issue 9, Pages 35–51
DOI: https://doi.org/10.3103/S1066369X18090050
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: Yu. K. Sabitova, “Dirichlet problem for Lavrent'ev–Bitsadze equation with loaded summands”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 9, 42–58; Russian Math. (Iz. VUZ), 62:9 (2018), 35–51
Citation in format AMSBIB
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\by Yu.~K.~Sabitova
\paper Dirichlet problem for Lavrent'ev--Bitsadze equation with loaded summands
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2018
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\pages 42--58
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\vol 62
\issue 9
\pages 35--51
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  • https://www.mathnet.ru/eng/ivm/y2018/i9/p42
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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