Abstract:
Within the framework of this work, solutions of boundary value problems with data on “opposite” (“parallel”) characteristics are found for one mixed-hyperbolic equation consisting of a wave operator in one part of the domain and a degenerate hyperbolic Gellerstedt operator in the other part. It is known that problems with data on opposite (parallel) characteristics for the wave equation in the characteristic quadrangle are posed incorrectly. However, as shown in this paper, the solution of similar problems for a mixed-hyperbolic equation consisting of a wave operator in one part of the domain and a degenerate hyperbolic Gellerstedt operator with an order of degeneracy in the other part of the domain, under certain conditions on the given functions, exists, is unique and is written explicitly.
Keywords:wave equation, degenerate hyperbolic equation, Volterra equation, Tricomi method, method of integral equations, methods of the theory of fractional calculus.
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