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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, Number 4, Pages 33–38 (Mi ivm1317)  
The Gellerstedt problem for a parabolic-hyperbolic equation of the 2nd kind

N. K. Mamadaliev

National University of Uzbekistan named after M. Ulugbek
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Abstract: In this paper we consider the Gellerstedt problem for a parabolic-hyperbolic equation of the 2nd kind. We prove the unique solvability of this problem, using the representation (obtained by the author) for a solution to the modified Cauchy problem in a generalized class $R$.
Keywords: generalized solution, mixed-type equation, Gellerstedt problem, gluing conditions.
Received: 18.12.2006
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2009, Volume 53, Issue 4, Pages 26–30
DOI: https://doi.org/10.3103/S1066369X09040045
Bibliographic databases:
UDC: 517.956
Language: Russian
Citation: N. K. Mamadaliev, “The Gellerstedt problem for a parabolic-hyperbolic equation of the 2nd kind”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 4, 33–38; Russian Math. (Iz. VUZ), 53:4 (2009), 26–30
Citation in format AMSBIB
\Bibitem{Mam09}
\by N.~K.~Mamadaliev
\paper The Gellerstedt problem for a~parabolic-hyperbolic equation of the 2nd kind
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2009
\issue 4
\pages 33--38
\mathnet{http://mi.mathnet.ru/ivm1317}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2581471}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2009
\vol 53
\issue 4
\pages 26--30
\crossref{https://doi.org/10.3103/S1066369X09040045}
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