论文标题
二维Riemann问题：跨性别冲击波和自由边界问题
Two-Dimensional Riemann Problems: Transonic Shock Waves and Free Boundary Problems
论文作者
论文摘要
我们关注的是多维Riemann问题的全球解决方案，用于非线性双曲线保护法，重点关注其全球配置和结构。我们在对二维Riemann问题的严格分析中介绍了一些最新进展，这些问题涉及跨性别的冲击波通过多双曲线的保护法的原型，并讨论了一些进一步的多维Riemann问题以及非线性偏微分方程的相关问题。特别是，我们通过双曲线系统的这些原型提出了四个不同的二维Riemann问题，并显示了如何将这些侵入问题的问题重新制定/解决，作为透射冲击波的自由边界问题，作为对相应的非线性保护法的自由边界问题，用于相应的非线性保护定律，这些法律是混合椭圆形的 - 纤维 - 磨损类型和相关的非线性部分差分差异方程。
We are concerned with global solutions of multidimensional 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 Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further multidimensional Riemann problems and related problems for nonlinear partial differential equations. In particular, we present four different two-dimensional 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.
