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Izv. Vyssh. Uchebn. Zaved. Mat., 2011, Number 2, Pages 54–64 (Mi ivm7233)  

This article is cited in 5 scientific papers (total in 5 papers)

One Goursat problem in a Sobolev space

I. G. Mamedov

Department "Mathematical modelling and prediction of antropogenetic processes", A. I. Guseinov Institute of Cybernetics, National Academy of Sciences, Republic of Azerbaijan, Baku, Republic of Azerbaijan

Abstract: In this paper we consider a hyperbolic-type differential equation with $L_p$-coefficients in a three-dimensional space. For this equation we study the Goursat problem with nonclassical boundary constraints not requiring matched conditions. We prove the equivalence of these boundary conditions to classical ones in the case when one seeks for a solution to the stated problem in an anisotropic space introduced by S. L. Sobolev. In addition, we prove the correct solvability of the Goursat problem by the method of integral equations.

Keywords: hyperbolic equation, three-dimensional Goursat problem, equations with $L_p$-coefficients.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:2, 46–55

Bibliographic databases:

UDC: 517.956
Received: 22.06.2009
Revised: 02.10.2009

Citation: I. G. Mamedov, “One Goursat problem in a Sobolev space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 2, 54–64; Russian Math. (Iz. VUZ), 55:2 (2011), 46–55

Citation in format AMSBIB
\Bibitem{Mam11}
\by I.~G.~Mamedov
\paper One Goursat problem in a~Sobolev space
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 2
\pages 54--64
\mathnet{http://mi.mathnet.ru/ivm7233}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2814821}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 2
\pages 46--55
\crossref{https://doi.org/10.3103/S1066369X1102006X}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79953020506}


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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. G. Mamedov, “Trekhmernaya integro-mnogotochechnaya kraevaya zadacha dlya nagruzhennykh volterro-giperbolicheskikh integro-differentsialnykh uravnenii tipa Bianki”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(26) (2012), 8–20  mathnet  crossref
    2. Mamedov I., “Neumann Problem in the Non-Classical Treatment for a Fourth Order Pseudoparabolic Equation”, 2012 IV International Conference Problems of Cybernetics and Informatics (Pci), ed. AidaZade K., IEEE, 2012  isi
    3. I. G. Mamedov, “Nonclassical Analog of the Goursat Problem for a Three-Dimensional Equation with Highest Derivative”, Math. Notes, 96:2 (2014), 239–247  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. I. G. Mamedov, “Nelokalnaya kombinirovannaya zadacha tipa Bitsadze–Samarskogo i Samarskogo–Ionkina dlya sistemy psevdoparabolicheskikh uravnenii”, Vladikavk. matem. zhurn., 16:1 (2014), 30–41  mathnet
    5. I. G. Mamedov, “O neklassicheskoi traktovke chetyrekhmernoi zadachi Gursa dlya odnogo giperbolicheskogo uravneniya”, Vladikavk. matem. zhurn., 17:4 (2015), 59–66  mathnet
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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