A system of partial differential equations describing the one-dimensional motion of an inviscid self-gravitating and spherical symmetric dusty gas cloud, is considered. Using the method of the kinematics of one-dimensional motion of shock waves, the evolution equation for the spherical shock wave of arbitrary strength in interstellar dusty gas clouds is derived. By applying first order truncation approximation procedure, an efficient system of ordinary differential equations describing shock propagation, which can be regarded as a good approximation of infinite hierarchy of the system. The truncated equations, which describe the shock strength and the induced discontinuity, are used to analyze the behavior of the shock wave of arbitrary strength in a medium of dusty gas. The results are obtained for the exponents from the successive approximation and compared with the results obtained by Guderley’s exact similarity solution and characteristic rule (CCW approximation). The effects of the parameters of the dusty gas and cooling-heating function on the shock strength are depicted graphically.

中文翻译：

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星际尘埃云中的一维球形冲击波

考虑了一个偏微分方程系统，该系统描述了无粘性的自重和球形对称粉尘状气体云的一维运动。利用冲击波的一维运动学方法，推导了星际尘埃云中任意强度的球形冲击波的演化方程。通过应用一阶截断近似程序，可以描述描述振动传播的常微分方程的有效系统，该系统可以视为系统无限层级的良好近似。截断方程描述了冲击强度和诱导的不连续性，用于分析含尘气体介质中任意强度的冲击波的行为。从逐次逼近获得指数的结果，并将其与通过Guderley的精确相似解和特征规则（CCW逼近）获得的结果进行比较。图形化地描述了粉尘气体和冷却-加热功能的参数对冲击强度的影响。