TWO DIMENSIONAL RIEMANN PROBLEMS FOR THE NONLINEAR WAVE SYSTEM: RAREFACTION WAVE INTERACTIONS

被引：5
作者：
Kim, Eun Heui [1 ]
Tsikkou, Charis [2 ]
机构：
[1] Calif State Univ Long Beach, Dept Math & Stat, Long Beach, CA 90840 USA
[2] West Virginia Univ, Dept Math, Morgantown, WV 26506 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2017年 / 37卷 / 12期
基金：
美国国家科学基金会;
关键词：
Rarefaction wave; transonic shock; Riemann problem; multidimensional conservation laws; nonlinear wave system; PRESSURE-GRADIENT SYSTEM; SEMI-HYPERBOLIC PATCHES; TRIPLE POINT PARADOX; GAS-DYNAMICS; TRANSONIC SHOCK; REGULAR REFLECTION; SUPERSONIC-FLOW; WEDGE; EQUATIONS; SCHEMES;
D O I：
10.3934/dcds.2017271
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We analyze rarefaction wave interactions of self-similar transonic irrotational flow in gas dynamics for two dimensional Riemann problems. We establish the existence result of the supersonic solution to the prototype nonlinear wave system for the sectorial Riemann data, and study the formation of the sonic boundary and the transonic shock. The transition from the sonic boundary to the shock boundary inherits at least two types of degeneracies (1) the system is sonic, and in addition (2) the angular derivative of the solution becomes zero where the sonic and shock boundaries meet.
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页码：6257 / 6289
页数：33
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