A complete global solution to the pressure gradient equation

被引：30
作者：
Lei, Zhen
Zheng, Yuxi [1 ]
机构：
[1] Penn State Univ, Dept Math, State Coll, PA 16802 USA
[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
[3] NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China
[4] Fudan Univ, Minist Educ, Key Lab Math Nonlinear Sci, Shanghai 200433, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2007年 / 236卷 / 01期
基金：
中国国家自然科学基金; 美国国家科学基金会;
关键词：
regularity; vacuum boundary; two-dimensional Riemann problem; characteristic decomposition; gas dynamics; shock waves; enter equations; Goursat problem;
D O I：
10.1016/j.jde.2007.01.024
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the domain of existence of a solution to a Riemann problem for the pressure gradient equation in two space dimensions. The Riemann problem is the expansion of a quadrant of gas of constant state into the other three vacuum quadrants. The global existence of a smooth solution was established in Dai and Zhang [Z. Dai, T. Zhang, Existence of a global smooth solution for a degenerate Goursat problem of gas dynamics, Arch. Ration. Mech. Anal. 155 (2000) 277-298] up to the free boundary of vacuum. We prove that the vacuum boundary is the coordinate axes. (C) 2007 Elsevier Inc. All rights reserved.
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页码：280 / 292
页数：13
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