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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, Number 5, Pages 44–52 (Mi ivm7302)  
This article is cited in 13 scientific papers (total in 13 papers)

The boundary-value problem for the Lavrent'ev–Bitsadze equation with unknown right-hand side

K. B. Sabitova, I. A. Khadzhib

a Laboratory of Differential Equations, Institute of Applied Research of Academy of Sciences of Republic Bashkortostan, Sterlitamak, Russia
b Chair of Mathematical Analysis, Sterlitamak State Pedagogical Academy, Sterlitamak, Russia
Full-text PDF (190 kB) Citations (13)
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Abstract: We study the inverse problem for the Lavrent'ev–Bitsadze equation in a rectangular domain. We construct its solution as a series in eigenfunctions for the corresponding problem on eigenvalues and establish a criterion for its uniqueness. We also prove the stability of the obtained solution.
Keywords: mixed-type equation, inverse problem, spectral method, uniqueness, existence, stability.
Received: 03.11.2009
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, Volume 55, Issue 5, Pages 35–42
DOI: https://doi.org/10.3103/S1066369X11050069
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: K. B. Sabitov, I. A. Khadzhi, “The boundary-value problem for the Lavrent'ev–Bitsadze equation with unknown right-hand side”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 5, 44–52; Russian Math. (Iz. VUZ), 55:5 (2011), 35–42
Citation in format AMSBIB
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\by K.~B.~Sabitov, I.~A.~Khadzhi
\paper The boundary-value problem for the Lavrent'ev--Bitsadze equation with unknown right-hand side
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 5
\pages 44--52
\mathnet{http://mi.mathnet.ru/ivm7302}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2920088}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 5
\pages 35--42
\crossref{https://doi.org/10.3103/S1066369X11050069}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80051604675}
Linking options:
  • https://www.mathnet.ru/eng/ivm7302
  • https://www.mathnet.ru/eng/ivm/y2011/i5/p44
    • This publication is cited in the following 13 articles:
    1. A. B. Bekiev, “Razreshimost nelokalnoi obratnoi zadachi dlya uravneniya chetvertogo poryadka”, Vestnik KRAUNTs. Fiz.-mat. nauki, 42:1 (2023), 9–26  mathnet  crossref
    2. A. B. Bekiev, R. M. Shykhyev, “Razreshimost kraevoi zadachi dlya smeshannogo uravneniya chetvertogo poryadka”, Doklady AMAN, 22:2 (2022), 11–20  mathnet  crossref  elib
    3. T. G. Ergashev, Z. R. Tulakova, “The Neumann Problem for a Multidimensional Elliptic Equation with Several Singular Coefficients in an Infinite Domain”, Lobachevskii J Math, 43:1 (2022), 199  crossref
    4. Yuldashev T.K. Islomov B.I. Abdullaev A.A., “On Solvability of a Poincare-Tricomi Type Problem For An Elliptic-Hyperbolic Equation of the Second Kind”, Lobachevskii J. Math., 42:3, SI (2021), 663–675  crossref  mathscinet  isi  scopus
    5. K. Sabitov, I. Burkhanova-Haji, “Reverse Problem to Find Right Parts Mixed Equations with the Chaplygin Operator”, Lobachevskii J Math, 42:15 (2021), 3726  crossref
    6. N. V. Martemyanova, “Nonlocal inverse problem to find unknown multipliers in right part of Lavrentev–Bitsadze equation”, Russian Math. (Iz. VUZ), 64:1 (2020), 40–57  mathnet  crossref  crossref  isi
    7. B. Yu. Irgashev, “On a boundary value problem for a high order mixed type equation”, Sib. elektron. matem. izv., 17 (2020), 899–912  mathnet  crossref
    8. K. B. Sabitov, N. V. Martemyanova, “K voprosu o korrektnosti obratnykh zadach dlya neodnorodnogo uravneniya Gelmgoltsa”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 22:2 (2018), 269–292  mathnet  crossref  zmath  elib
    9. K. B. Sabitov, N. V. Martem'yanova, “Inverse problem for Lavrent'ev–Bitsadze equation connected with the search of elements in right-hand side”, Russian Math. (Iz. VUZ), 61:2 (2017), 36–48  mathnet  crossref  isi
    10. K. B. Sabitov, G. Yu. Udalova, “Kraevaya zadacha dlya uravneniya smeshannogo tipa tretego poryadka s usloviyami periodichnosti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 3(32) (2013), 29–45  mathnet  crossref  zmath
    11. I. A. Khadzhi, “Inverse Problem for Equations of Mixed Type with Lavrentev–Bitsadze Operator”, Math. Notes, 91:6 (2012), 857–867  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    12. Udalova G.Yu., “Obratnaya zadacha dlya uravneniya s operatorom Lavrenteva-Bitsadze”, Doklady Adygskoi akademii nauk, 14:1 (2012), 98–110  elib
    13. Udalova G.Yu., “Kraevaya zadacha dlya uravneniya Lavrenteva-Bitsadze s neizvestnoi pravoi chastyu”, Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. seriya: matematika. fizika, 26:5 (2012), 207–223  elib
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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