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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, Number 9, Pages 42–58 (Mi ivm9396)  
This article is cited in 7 scientific papers (total in 7 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 (7)
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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
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\yr 2018
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\pages 42--58
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\vol 62
\issue 9
\pages 35--51
\crossref{https://doi.org/10.3103/S1066369X18090050}
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Linking options:
  • https://www.mathnet.ru/eng/ivm9396
  • https://www.mathnet.ru/eng/ivm/y2018/i9/p42
    • This publication is cited in the following 7 articles:
    1. V. I. Korzyuk, J. V. Rudzko, “Classical solution of the Cauchy problem for a semilinear wave equation with a Dirac potential”, Dokl. Akad. nauk, 69:1 (2025), 7  crossref
    2. B. I. Islomov, T. K. Yuldashev, O. M. Yunusov, “Nonlocal Boundary Problem for a Loaded Equation of Mixed Type in a Special Domain”, Lobachevskii J Math, 45:7 (2024), 3304  crossref
    3. B. I. Islomov, F. M. Juraev, “Local boundary value problems for a loaded equation of parabolic-hyperbolic type degenerating inside the domain”, Ufa Math. J., 14:1 (2022), 37–51  mathnet  crossref  mathscinet
    4. K. U. Khubiev, “Kraevye zadachi dlya kharakteristicheski nagruzhennogo uravneniya giperbolo-parabolicheskogo tipa”, Materialy mezhdunarodnoi konferentsii po matematicheskomu modelirovaniyu v prikladnykh naukakh “International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19”. Belgorod, 20–24 avgusta 2019 g., Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 195, VINITI RAN, M., 2021, 127–138  mathnet  crossref
    5. K. U. Khubiev, “Zadacha Bitsadze—Samarskogo dlya nagruzhennogo giperbolo-parabolicheskogo uravneniya c vyrozhdeniem poryadka v oblasti ego giperbolichnosti”, Differentsialnye uravneniya i matematicheskaya fizika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 198, VINITI RAN, M., 2021, 123–132  mathnet  crossref
    6. T. K. Yuldashev, B. I. Islomov, U. Sh. Ubaydullaev, “On boundary value problems for a mixed type fractional differential equation with Caputo operator”, Bull. Karaganda Univ-Math., 101:1 (2021), 127–137  crossref  mathscinet  isi
    7. E. Providas, I. N. Parasidis, Springer Optimization and Its Applications, 179, Mathematical Analysis in Interdisciplinary Research, 2021, 641  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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