Geodesic
Problems with shifts for mixed elliptic-hyperbolic equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2012), pp. 72-82

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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, integral equations, index of equation.
Mots-clés : singular coefficient 
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     author = {M. Kh. Ruziev},
     title = {Problems with shifts for mixed elliptic-hyperbolic equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {72--82},
     publisher = {mathdoc},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_1_a9/}
}
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M. Kh. Ruziev. Problems with shifts for mixed elliptic-hyperbolic equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2012), pp. 72-82. http://geodesic.mathdoc.fr/item/IVM_2012_1_a9/