A boundary-value problem with shift for a hyperbolic equation degenerate in the interior of a region

Abstract

For a degenerate hyperbolic equation in characteristic region (lune) a boundary-value problem with operators of fractional integro-differentiation is studied. The solution of this equation on the characteristics is related point-to-point to the solution and its derivative on the degeneration line. The uniqueness theorem is proved by the modified Tricomi method with inequality-type constraints on the known functions. Question of the problem solution's existence is reduced to the solvability of a singular integral equation with Cauchy kernel of the normal type.

Keywords

• cauchy problem
• boundary-value problem with shift
• fractional integro-differentiation operators
• singular equation with cauchy kernel
• regularizer
• gauss hypergeometric function
• euler gamma function