Mathematical modeling and analysis of astronomical phenomena on the basis of continuum approximation

在连续统近似的基础上，对包括天体内部现象在内的一些天体物理现象进行了数学建模，并对其进行了数学分析。我们得到了以下两个主要结果：(1)在理想气体构成的恒星，其运动是空间一维的情况下，我们找到了一个关于恒星外部环境的条件，保证气体运动长期稳定地存在；(2)在气体运动为球对称的三维情况下，我们得到了与(1)近似等效的结果。虽然我们的研究已经有了先例，但我们还是在一些要点上进行了改进。

We mathematically modelized, on the basis of continuum approximation, some astrophysical phenomena including the inner one of astronomical bodies, and mathematically analyzed them. We obtained the following main two results: (1) On the case that a star is composed by the ideal gas and its motion is spacially one-dimensional, we found a certain condition, concerning external circumstances of the star, guaranteeing that the motion of the gas exists long-time and stably; (2) On the case that the gaseous motion is spherically symmetric in three-dimension, we obtained the result nearly equivalent to the one in (1). Although a precedent result of our study has already been obtained by the present reporter, we succeeded in refining them at some essential points.