Two-Dimensional Riemann Problems: Transonic Shock Waves and Free Boundary Problems
Two-Dimensional Riemann Problems: Transonic Shock Waves and Free Boundary Problems
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DOI：
10.1007/s42967-022-00210-4
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发表时间：
2022-04
影响因子：
1.6
通讯作者：
Gui-Qiang G. Chen
中科院分区：
文献类型：
--
作者：
Gui-Qiang G. Chen
本文主要研究非线性双曲守恒律方程组的多维（M-D）Riemann问题的整体解，重点研究其整体构型和结构。本文通过几个双曲型守恒律组的原型，介绍了关于跨音速激波的二维Riemann问题的严格分析的一些最新进展，并进一步讨论了非线性偏微分方程的M-D Riemann问题和相关问题。特别是，我们提出了四个不同的2-D黎曼问题，通过这些原型的双曲型系统，并显示这些黎曼问题可以重新制定/解决为自由边界问题的跨音速激波作为自由边界的相应的非线性守恒律的混合椭圆-双曲型和相关的非线性偏微分方程。
We are concerned with global solutions of multidimensional (M-D) Riemann problems for nonlinear hyperbolic systems of conservation laws, focusing on their global configurations and structures. We present some recent developments in the rigorous analysis of two-dimensional (2-D) Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations. In particular, we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.