zbMATH — the first resource for mathematics

On the existence and uniqueness of the solution of a nonclassical boundary value problem. (English. Russian original) Zbl 0836.35101
Russ. Acad. Sci., Dokl., Math. 49, No. 3, 532-535 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 336, No. 4, 448-450 (1994).
In this note we investigate the solvability of a nonclassical boundary value problem of generalized Tricomi type for an elliptic-hyperbolic equation like those considered in [A. G. Kuz’min, Nonclassical equations of mixed type and their applications to gas dynamics, Izdat. Leningrad. Univ., Leningrad (1990; Zbl 0745.35026); rev. English transl., Birkhäuser, Basel (1992)], §3.6. We show for which opening angles of the domain the problem is uniquely solvable, and for which angles no solution exists. The existence of the solution is established with the help of biorthogonal series with respect to a system of sines and cosines.

35M10 PDEs of mixed type
76N15 Gas dynamics, general