论文标题
埃勒方程的利曼问题具有单数来源
Riemann problem of Euler equations with singular sources
论文作者
论文摘要
本文关注的是具有单数来源的一维欧拉方程的黎曼问题。 这个Riemann问题的确切解决方案包含奇异源引起的固定不连续性，该不连续性与经典Euler方程的Riemann解决方案中的所有简单波动不同。 我们提出了一个基于特征值的单调性标准，以选择这种固定不连续性的物理曲线。 通过将这种固定的不连续性作为基本波，Riemann溶液的结构变为多样化，例如波的数量不是固定的，并且两个波之间的相互作用是可能的。 在双重CRP框架下，我们证明了Riemann解决方案的所有可能结构。
This paper is concerned with the Riemann problem of one-dimensional Euler equations with a singular source. The exact solution of this Riemann problem contains a stationary discontinuity induced by the singular source, which is different from all the simple waves in the Riemann solution of classical Euler equations. We propose an eigenvalue-based monotonicity criterion to select the physical curve of this stationary discontinuity. By including this stationary discontinuity as an elementary wave, the structure of Riemann solution becomes diverse, e.g. the number of waves is not fixed and interactions between two waves become possible. Under the double CRP framework, we prove all possible structures of the Riemann solution.
