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Boundary value problem for a particular form of the Euler-Darboux equation with integral conditions and special conjugation conditions on characteristic. (English. Russian original) Zbl 1011.35101
Russ. Math. 44, No. 8, 14-17 (2000); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2000, No. 8, 16-19 (2000).
The paper deals with the Euler-Poisson-Darboux equation when a constant coefficient of the term containing the first derivative with respect to \(y\) equals to zero. It is considered in the domain consisting of a rectangle and triangle with common side \(x=0,\) \(0<y<h\) (which lies on a characteristic) and sides lying on the line \(y=h.\) On the side of the triangle lying on the line \(y=x\) the equation is order degenerated. Under some restrictions the unique solution of the equation with some integral conditions (so-called nonlocal boundary conditions), and conjugation conditions on the above characteristic is explicitly constructed.

35Q05 Euler-Poisson-Darboux equations
35L80 Degenerate hyperbolic equations