Self-similar viscosity approach to the Riemann problem for a strictly hyperbolic system of conservation laws

被引：5

作者：

Chhatria, Balakrishna ^{[1
]}

Sen, Anupam ^{[2
]}

Sekhar, T. Raja ^{[1
]}

机构：

[1] Indian Inst Technol Kharagpur, Dept Math, Kharagpur, India

[2] Tata Inst Fundamental Res, Ctr Applicable Math, Bangalore, India

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2023年 / 46卷 / 06期

关键词：

delta shock wave; Riemann problem; self-similar vanishing viscosity; strictly hyperbolic system; DELTA-SHOCK-WAVES; VANISHING PRESSURE LIMIT; EULER EQUATIONS; STABILITY; CAVITATION;

D O I：

10.1002/mma.8969

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Here, we study the Riemann problem for a strictly hyperbolic system of conservation laws, which occurs in gas dynamics and nonlinear elasticity. We establish the existence and uniqueness of the solution of Riemann problem containing delta shock wave by employing self-similar vanishing viscosity approach. We prove that delta shock is stable under self-similar viscosity perturbation, which ensures that delta shock wave is a unique entropy solution.

引用

页码：7265 / 7284

页数：20

共 50 条

[31] RIEMANN PROBLEM FOR A NON-STRICTLY HYPERBOLIC SYSTEM IN CHEMOTAXIS
Li, Tong
Mathur, Nitesh
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2022, 27 (04): : 2173 - 2187
[32] The Riemann problem with delta initial data for a class of coupled hyperbolic systems of conservation laws
Yang, Hanchun
Sun, Wenhua
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 67 (11) : 3041 - 3049
[33] Uniqueness of self-similar solutions to the Riemann problem for the Hopf equation with complex nonlinearity
Kulikovskii, A. G.
Chugainova, A. P.
Shargatov, V. A.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2016, 56 (07) : 1355 - 1362
[34] Multidimensional Riemann problem with self-similar internal structure - part III - a multidimensional analogue of the HLLI Riemann solver for conservative hyperbolic systems
Balsara, Dinshaw S.
Nkonga, Boniface
JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 346 : 25 - 48
[35] Global solutions with shock waves to the generalized Riemann problem for a system of hyperbolic conservation laws with linear damping
Shao, Zhi-Qiang
Kong, De-Xing
Li, Ya-Chun
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 325 (02) : 843 - 865
[36] Global structure of Riemann solutions to a system of two-dimensional hyperbolic conservation laws
Shen, Chun
Sun, Meina
Wang, Zhen
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (14) : 4754 - 4770
[37] Eigenvalues of self-similar solutions of the dafermos regularization of a system of conservation laws via geometric singular perturbation theory
Schecter, Stephen
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2006, 18 (01) : 53 - 101
[38] THE RIEMANN PROBLEM OF CONSERVATION LAWS IN MAGNETOGASDYNAMICS
Hu, Yanbo
Sheng, Wancheng
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2013, 12 (02) : 755 - 769
[39] Hyperbolic systems of conservation laws with Lipschitz continuous flux-functions: The Riemann problem
Correia, J
LeFloch, PG
Thanh, MD
BOLETIM DA SOCIEDADE BRASILEIRA DE MATEMATICA, 2001, 32 (03): : 271 - 301
[40] Hyperbolic systems of conservation laws with Lipschitz continuous flux-functions: The Riemann problem
Joaquim Correia
Philippe G. LeFloch
Mai Duc Thanh
Boletim da Sociedade Brasileira de Matemática - Bulletin/Brazilian Mathematical Society, 2001, 32 : 271 - 301

← 1 2 3 4 5 →