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Izv. Vyssh. Uchebn. Zaved. Mat., 2011, Number 5, Pages 44–52 (Mi ivm7302)  

This article is cited in 8 scientific papers (total in 8 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

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.

Full text: PDF file (190 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:5, 35–42

Bibliographic databases:

UDC: 517.95
Received: 03.11.2009

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
\Bibitem{SabKha11}
\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://www.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}


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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. 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
    2. Udalova G.Yu., “Obratnaya zadacha dlya uravneniya s operatorom Lavrenteva-Bitsadze”, Doklady Adygskoi akademii nauk, 14:1 (2012), 98–110  elib
    3. 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
    4. 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
    5. 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
    6. 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
    7. N. V. Martemyanova, “Obratnaya zadacha dlya uravneniya Lavrenteva–Bitsadze po opredeleniyu somnozhitelei pravoi chasti”, Izv. vuzov. Matem., 2020, no. 1, 46–63  mathnet  crossref
    8. 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
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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