带抛物退化线的一阶混合型复方程的间断Riemann-Hilbert问题

有些作者提出和讨论了在一些特殊区域上二阶混合型方程的Tricomi问题．本文讨论带抛物退化线的一阶混合型(椭圆-双曲)型复方程的间断Riemann-Hilbert边值问题．先给出这个问题的提法和解的表示式，然后使用复分析方法，即在椭圆区域使用复变函数，而在双曲区域使用双曲复函数，证明了上述混合型方程Riemann-Hilbert问题解的存在唯一性。

The Discontinuous Riemann-Hilbert Problem for First Order Mixed Complex Equations With Parabolic Degeneracy

The Tricomi problem of second order equations of mixed type in a special domain was posed and discussed by previous authors,The present paper deals with the discontinuous Riemann-Hilbert problem for first order complex equations of mixed(elliptic-hyperbolic) type with parabolic degeneracy. Firstly,the formulation of the above boundary value problem is given, and then the existence of solutions for the above problem is proved, in which the complex analytic method, i.e. the complex functions in the elliptic domain and the hyperbolic complex functions in the hyperbolic domain is used.