Geodesic
A~Boundary-value Problem with Shift for a~Hyperbolic Equation Degenerate in the Interior of a~Region
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2014), pp. 37-47

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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. 
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     author = {O. A. Repin and S. K. Kumykova},
     title = {A~Boundary-value {Problem} with {Shift} for {a~Hyperbolic} {Equation} {Degenerate} in the {Interior} of {a~Region}},
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O. A. Repin; S. K. Kumykova. A~Boundary-value Problem with Shift for a~Hyperbolic Equation Degenerate in the Interior of a~Region. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2014), pp. 37-47. http://geodesic.mathdoc.fr/item/VSGTU_2014_1_a3/