In this article, we study the delta shock wave for zero-pressure gasdynamics system with energy conservation laws in the frame of \(\alpha \)-solutions defined in the setting of distributional products. By reformulating the system, we construct within a convenient space of distributions, all solutions which include discontinuous solutions and Dirac delta measures. We also establish the generalized Rankine–Hugoniot jump conditions for delta shock waves. The \(\alpha \)-solutions which we constructed coincide with the solution obtained through different methods.

中文翻译：

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零压力气体动力学系统中具有节能规律的三角波研究中的分布相乘

在本文中，我们以配电产品设置中定义的\（\ alpha \）-解为框架，研究了具有节能规律的零压力气体动力学系统的三角波冲击波。通过重新构建系统，我们在一个方便的分布空间中构造了所有解决方案，包括不连续解决方案和狄拉克增量测量。我们还为三角波冲击波建立了广义的兰金-Hugoniot跳跃条件。我们构造的\（\ alpha \）-解决方案与通过不同方法获得的解决方案一致。