In this article, a system of partial differential equations governing the one‐dimensional motion of inviscid, self‐gravitating, spherical dusty gas cloud is considered. The evolutionary behavior of spherical shock waves of arbitrary strength in an interstellar dusty gas cloud is examined. By utilizing the method based on the kinematics of the one‐dimensional motion of shock waves, we derived an infinite set of transport equations governing the strength of shock waves and induced discontinuity behind it. By applying the truncation procedure to the infinite set of transport equations, we get an efficient system of finite number ordinary differential equations describing shock propagation, which can be regarded as a good approximation of the infinite hierarchy of the system. The truncated equations describing the shock strength and the induced discontinuity are used to analyze the growth and decay behavior of shock waves of arbitrary strength in the dusty gas medium. We considered the first two truncation approximations and the obtained results for the exponent from the successive approximation and compared our results with Guderley's exact similarity solution and the characteristic rule.

中文翻译：

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星际理想气体云中带有尘埃粒子的球形冲击波的运动学

在本文中，考虑了一个偏微分方程系统，该系统控制无粘性，自重，球形尘土气团的一维运动。研究了星际尘埃云中任意强度的球形冲击波的演化行为。通过利用基于冲击波一维运动的运动学的方法，我们导出了控制冲击波强度并在其后引起不连续性的无穷多输运方程集。通过将截断程序应用于无穷大的输运方程组，我们得到了一个描述冲击传播的有限数量的常微分方程组的有效系统，可以将其视为系统无限级数的良好近似。截断方程描述了冲击强度和诱导的不连续性，用于分析尘埃气体介质中任意强度的冲击波的增长和衰减行为。我们考虑了前两个截断逼近以及从逐次逼近获得的指数结果，并将我们的结果与Guderley的精确相似性解和特征规则进行了比较。