几类一阶双曲型方程组的复形式及其解的存在唯一性

The Complex Form of Some Hyperbolic Systems of First Order Equations and Existence and Uniqueness of its Solution

先引入双曲数和双曲函数,它们分别对应于复数与复变函数,然后以此为基础,把平面区域内几类两个实自变量、两个实未知函数的一阶拟线性双曲型方程组化为复形式,这种复形式的方程(简称复方程)与文献中的复方程有所不同。其次,我们使用逐次逼近法与Schauder不动点定理证明在一定条件下的上述复方程存在唯一解。

In this paper, we first introduce the hyperbolic numbers and hyperbolic functions in [1]and[2], which correspond complex numbers and complex functions respectively with two real variable numbers and two real unknown functions into the complex form, which is different to complex equations in [3]. Secondly, by using the method of succeSSive approximation and Schauder fixed point theorem we prove the existence and uniqueneSS of solution Of the above complex equations with certain conditions.