STRUCTURAL STABILITY OF SOLUTIONS TO THE RIEMANN PROBLEM FOR A SCALAR NONCONVEX CJ COMBUSTION MODEL

被引：17

作者：

Sheng, Wancheng ^{[1
]}

Zhang, Tong ^{[2
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

[2] Chinese Acad Sci, AMSS, Inst Math, Beijing 100080, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2009年 / 25卷 / 02期

关键词：

Scalar nonconvex C-J combustion model; pointwise and global entropy conditions; structural stability; Riemann problem; transition from deflagration to detonation; DYNAMIC COMBUSTION; REACTING GAS; TRANSITION;

D O I：

10.3934/dcds.2009.25.651

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Riemann problem for the simplest scalar nonconvex CJ combustion model is considered. A set of entropy conditions are summarized, including pointwise entropy conditions and global entropy conditions. The later is according to the requirement of the structural stability. The unique self-similar entropy solution of the Riemann problem is constructed case by case. Transition from deflagration to detonation is shown, which dose not occur for the convex model.

引用

页码：651 / 667

页数：17

共 25 条

[1] THE GENERALIZED RIEMANN PROBLEM FOR A SCALAR NONCONVEX COMBUSTION MODEL-THE PERTURBATION ON INITIAL BINDING ENERGY
Pan Lijun
Sheng Wancheng
ACTA MATHEMATICA SCIENTIA, 2012, 32 (03) : 1262 - 1280
[2] The generalized riemann problem for a scalar nonconvex chapman-jouguet combustion model
Sheng, Wancheng
Sun, Meina
Zhang, Tong
SIAM JOURNAL ON APPLIED MATHEMATICS, 2007, 68 (02) : 544 - 561
[3] Structural stability of solutions to the Riemann problem for a scalar conservation law
Shen, Chun
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 389 (02) : 1105 - 1116
[4] The generalized Riemann problem for a scalar Chapman-Jouguet combustion model
Sun, Meina
Sheng, Wancheng
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2009, 60 (02): : 271 - 283
[5] Perturbed Riemann Problem for a Scalar Chapman-Jouguet Combustion Model
Sun, Meina
CHINESE ANNALS OF MATHEMATICS SERIES B, 2015, 36 (02) : 267 - 278
[6] ON THE RIEMANN PROBLEM FOR A SCALAR ZELDOVICH-VON NEUMANN-DORING COMBUSTION MODEL
Lai, Geng
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2014, 46 (04) : 2404 - 2443
[7] Instability of unburnt gas for a scalar nonconvex combustion model
Liu, Yujin
Sheng, Wancheng
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2012, 13 (01) : 1 - 13
[8] Geometric solutions of the Riemann problem for the scalar conservation law
Palin, V. V.
VESTNIK SAMARSKOGO GOSUDARSTVENNOGO TEKHNICHESKOGO UNIVERSITETA-SERIYA-FIZIKO-MATEMATICHESKIYE NAUKI, 2018, 22 (04): : 620 - 646
[9] STRUCTURAL STABILITY OF SOLUTIONS TO THE RIEMANN PROBLEM FOR A NON-STRICTLY HYPERBOLIC SYSTEM WITH FLUX APPROXIMATION
Sun, Meina
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2016,
[10] Singular solutions to the Riemann problem for a macroscopic production model
Sun, Meina
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2017, 97 (08): : 916 - 931

← 1 2 3 →