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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, Number 2, Pages 54–64 (Mi ivm7233)  
This article is cited in 7 scientific papers (total in 7 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
Full-text PDF (210 kB) Citations (7)
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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.
Received: 22.06.2009
Revised: 02.10.2009
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, Volume 55, Issue 2, Pages 46–55
DOI: https://doi.org/10.3103/S1066369X1102006X
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
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://mathscinet.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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79953020506}
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    • This publication is cited in the following 7 articles:
    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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    Full-text PDF :121
    References:120
    First page:31
     
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