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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, Number 11, Pages 44–53 (Mi ivm9051)  
This article is cited in 4 scientific papers (total in 4 papers)

The Dirichlet problem for an equation of mixed elliptic-hyperbolic type with variable potential

N. V. Martem'yanova

Chair of Mathematics and Teaching Principles, Volga Region Social-Humanitarian Academy, 26 Antonov-Ovseenko str., Samara, 443090 Russia
Full-text PDF (198 kB) Citations (4)
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Abstract: We study the Dirichlet problem for an equation of mixed elliptic-hyperbolic type with variable potential in the rectangular area. We establish a criterion of the uniqueness of a solution to this problem. The uniqueness of a solution is proved on the basis of the completeness of systems of functions corresponding to one-dimensional spectral problem. Solution was constructed as a sum of series on the systems of eigenfunctions. The existence is proved under certain conditions upon the ratio of the rectangle sides of hyperbolic part of the equation, upon the boundary functions and function of potential.
Keywords: mixed type equation, Dirichlet problem, spectral method, uniqueness, small denominators, existence.
Received: 07.04.2014
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, Volume 59, Issue 11, Pages 36–44
DOI: https://doi.org/10.3103/S1066369X15110043
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: N. V. Martem'yanova, “The Dirichlet problem for an equation of mixed elliptic-hyperbolic type with variable potential”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 11, 44–53; Russian Math. (Iz. VUZ), 59:11 (2015), 36–44
Citation in format AMSBIB
\Bibitem{Mar15}
\by N.~V.~Martem'yanova
\paper The Dirichlet problem for an equation of mixed elliptic-hyperbolic type with variable potential
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2015
\issue 11
\pages 44--53
\mathnet{http://mi.mathnet.ru/ivm9051}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2015
\vol 59
\issue 11
\pages 36--44
\crossref{https://doi.org/10.3103/S1066369X15110043}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84945176438}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    References:30
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