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：

美国国家科学基金会; 中国国家自然科学基金;

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.

引用

页码：280 / 292

页数：13

共 18 条

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[2]

[Anonymous], ACTA MATH APPL SIN E

[3]

[Anonymous], ACTA MATH APPL SIN+

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