第一部分，研究无界外区域双曲型初边值问题基于自然边界归化的人工边界条件及其数值方法。
Part I, the artificial boundary condition and its numerical methods based on natural boundary reduction for hyperbolic initial boundary value problems on unbounded domains is studied.
研究具有变动边界的三维区域上的非线性双曲型方程的初边值问题。
The initial boundary value problem for nonlinear hyperbolic equation in three dimensional domain with moving boundary is studied.
本文以两个自变量的拟线性双曲型方程的古尔沙问题为例，应用反函数和积分不等式证明了等价积分方程组解的存在唯一性，同时给出了解的存在区域和已知参量的依赖关系。
In this paper, we show the domain of the existence of the solution on Goursat problem for quasi—linear hyperbolic equation and obtain the Theorem of the existence and uniqueness in above domain.
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