无压气体动力学的概率模型
Probabilistic model associated with the pressureless gas dynamics
摘要：
本文利用Langevin系统的随机扰动方法和非粘性Burgers方程，构造了粘性粒子无压气体动力学黎曼问题的一个解。作为桥接步骤，我们考虑由非相互作用粒子组成的介质。我们分析了这两个模型的间断解行为的差异以及它们之间的联系。在我们的框架中，我们得到了一个唯一的熵解的黎曼问题在一维情况下。此外，我们描述了如何从光滑的数据开始的$δ$奇异性出现在一个组件的解决方案。
英文摘要：
Using a method of stochastic perturbation of a Langevin system associated with the non-viscous Burgers equation we construct a solution to the Riemann problem for the pressureless gas dynamics describing sticky particles. As a bridging step we consider a medium consisting of noninteracting particles. We analyze the difference in the behavior of discontinuous solutions for these two models and the relations between them. In our framework we obtain a unique entropy solution to the Riemann problem in 1D case. Moreover, we describe how starting from smooth data a $δ$ - singularity arises in one component of the solution.
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