Problems with shifts for mixed elliptic-hyperbolic equations

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 menti...

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Bibliographic Details
Published in:Russian mathematics 2012, Vol.56 (1), p.66-75
Main Author: Ruziev, M. Kh
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X12010100