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Izv. Vyssh. Uchebn. Zaved. Mat., 2012, Number 1, Pages 72–82 (Mi ivm8422)  

This article is cited in 2 scientific papers (total in 2 papers)

Problems with shifts for mixed elliptic-hyperbolic equations

M. Kh. Ruziev

Department of Differential Equations, Institute of Mathematics and Information Technologies, Uzbekistan Academy of Sciences, Tashkent, Republic of Uzbekistan

Abstract: In this paper we study a problem with a shift, where some characteristics are free from boundary conditions; the absent V. I. Zhegalov and A. M. Nakhushev conditions are replaced with an analog of F. Frankl condition on a segment of the degeneration line. We prove the unique solvability of the mentioned problem with the help of the extremum principle. The proof of the solvability is based on the theory of singular integral equations, Wiener–Hopf equations and Fredholm integral equations.

Keywords: principle of extremum, unique solvability, solvability, singular coefficient, integral equations, index of equation.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:1, 66–75

Bibliographic databases:

UDC: 517.956
Received: 28.12.2010

Citation: M. Kh. Ruziev, “Problems with shifts for mixed elliptic-hyperbolic equations”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 1, 72–82; Russian Math. (Iz. VUZ), 56:1 (2012), 66–75

Citation in format AMSBIB
\Bibitem{Ruz12}
\by M.~Kh.~Ruziev
\paper Problems with shifts for mixed elliptic-hyperbolic equations
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2012
\issue 1
\pages 72--82
\mathnet{http://mi.mathnet.ru/ivm8422}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2975921}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2012
\vol 56
\issue 1
\pages 66--75
\crossref{https://doi.org/10.3103/S1066369X12010100}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84862702717}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Feng Zh., Kuang J., “Boundary Value Problem for a Nonlinear Equation of Mixed Type”, J. Differ. Equ., 255:10 (2013), 3029–3052  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Ruziev M.Kh., “A Problem with Conditions Given on Inner Characteristics and on the Line of Degeneracy for a Mixed-Type Equation with Singular Coefficients”, Bound. Value Probl., 2013, 210  crossref  mathscinet  zmath  isi  elib  scopus
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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