Problem with lacking Tricomi condition on a characteristic and an analog of the Frankl condition on a segment of the degeneration line for a class of mixed type equations

For the Gellerstedt equation with a singular coefficient, we consider a boundary value problem that differs from the Tricomi problem in that the boundary characteristic AC is arbitrarily divided into two parts AC 0 and C 0 C and the Tricomi condition is posed on the first of them, while the second part C 0 C is free of boundary conditions. The lacking Tricomi condition is equivalently replaced by an analog of the Frankl condition on a segment of the degeneration line. The well-posedness of this problem is proved.

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