Abstract

In this paper, the unique solvability of the Cauchy problem for a generalized hyperbolic Gellersted equation with two lines of degeneracy of different order is studied. A modified initial problem is formulated. By using the Riemann method the solution of this problem is constructed in an explicit form inside characteristic triangle. The constructed Riemann function is expressed by special Appell functions and Gauss hypergeometric functions of two variables.

中文翻译：

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广义Gellerstedt方程Cauchy问题的解。

摘要

本文研究了具有两阶不同阶简并性的广义双曲Gellersted方程的柯西问题的唯一可解性。提出了修改后的初始问题。通过使用黎曼方法，可以在特征三角形内部以显式形式构造此问题的解决方案。构造的黎曼函数由两个变量的特殊Appell函数和高斯超几何函数表示。