A Boundary-value Problem with Shift for a Hyperbolic Equation Degenerate in the Interior of a Region

• Main Authors: Oleg A. Repin, Svetlana K. Kumykova
• Format: Article
• Language: English
• Published: Samara State Technical University 2014-03-01
• Series: Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki
• Subjects: Cauchy problem; boundary-value problem with shift; fractional integro-differentiation operators; singular equation with Cauchy kernel; regularizer; Gauss hypergeometric function; Euler gamma function
• Online Access: http://mi.mathnet.ru/eng/vsgtu1280

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.