On a Problem with Shift on Pieces of Boundary Characteristics for the Gellerstedt Equation with Singular Coefficients.

In this paper we study a problem with local displacement conditions on a segment of the degeneration line and with displacements on pieces of boundary characteristics in an unbounded domain, the elliptical part of which is the upper half-plane, and the hyperbolic part is the characteristic triangle. The uniqueness of the solution of the problem is proved using the extremum principle. The proof of the existence is based on the theory of singular integral equations, Wiener–Hopf equations, and Fredholm integral equations. [ABSTRACT FROM AUTHOR]