The limits of Riemann solutions for the isentropic Euler system with extended Chaplygin gas

被引：10

作者：

Tong, Meizi ^{[1
]}

Shen, Chun ^{[1
]}

机构：

[1] Ludong Univ, Sch Math & Stat Sci, Yantai 264025, Peoples R China

来源：

APPLICABLE ANALYSIS | 2019年 / 98卷 / 15期

关键词：

Extended Chaplygin gas; Chaplygin gas; delta shock wave; Riemann problem; isentropic Euler system; VANISHING PRESSURE LIMIT; DELTA-SHOCK-WAVES; VACUUM STATES; HYPERBOLIC SYSTEMS; EQUATIONS; PROPAGATION; DYNAMICS;

D O I：

10.1080/00036811.2018.1469009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Riemann problem for the isentropic Euler system with the state equation for the extended Chaplygin gas is considered, and the Riemann solutions are constructed completely for all the cases. The limiting relations of Riemann solutions for the isentropic Euler system with the state equation from the extended Chaplygin gas to the Chaplygin gas are derived in detail when the corrected term tends to zero. The formation of delta shock wave solution and two-contact-discontinuity solution is investigated during the process of taking the limit.

引用

页码：2668 / 2687

页数：20

共 40 条

[1]

[Anonymous], 2012, SHOCK WAVES REACTION

[2]

[Anonymous], PREPRINT

[3]

[Anonymous], ARXIV170705153V1

[4] Generalized Chaplygin gas, accelerated expansion, and dark-energy-matter unification [J].

Bento, MC ;

Bertolami, O ;

Sen, AA .

PHYSICAL REVIEW D, 2002, 66 (04)

[5] Unification of dark matter and dark energy: the inhomogeneous Chaplygin gas [J].

Bilic, N ;

Tupper, GB ;

Viollier, RD .

PHYSICS LETTERS B, 2002, 535 (1-4) :17-21

[6] Solutions with concentration to the Riemann problem for the one-dimensional chaplygin gas equations [J].

Brenier, Y .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2005, 7 (Suppl 3) :S326-S331

[7]

Chaplygin S, 1904, Sci Mem Moscow Univ Math Phys, V21, P1

[8] Formation of δ-shocks and vacuum states in the vanishing pressure limit of solutions to the Euler equations for isentropic fluids [J].

Chen, GQ ;

Liu, HL .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2003, 34 (04) :925-938

[9] THE RIEMANN PROBLEM AND THE LIMIT SOLUTIONS AS MAGNETIC FIELD VANISHES TO MAGNETOGASDYNAMICS FOR GENERALIZED CHAPLYGIN GAS [J].

Chen, Jianjun ;

Sheng, Wancheng .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2018, 17 (01) :127-142

[10] Delta shock wave formation in the case of triangular hyperbolic system of conservation laws [J].

Danilov, V. G. ;

Mitrovic, D. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 245 (12) :3704-3734

← 1 2 3 4 →