American Institute of Mathematical Sciences

Advanced
July  2009, 25(2): 651-667. doi: 10.3934/dcds.2009.25.651

Structural stability of solutions to the Riemann problem for a scalar nonconvex CJ combustion model

Wancheng Sheng 1, and  Tong Zhang 2,

1. 

Department of Mathematics, Shanghai University, Shanghai, 200444, China
2. 

Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100080, China

Received  January 2008 Revised  February 2009 Published  June 2009

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.
Keywords: pointwise and global entropy conditions, transition from deflagration to detonation., Scalar nonconvex C-J combustion model, structural stability, Riemann problem.
Mathematics Subject Classification: 35L45, 35L60, 35L65, 35L67, 58J45, 76L05, 76N10, 80A2.
Citation: Wancheng Sheng, Tong Zhang. Structural stability of solutions to the Riemann problem for a scalar nonconvex CJ combustion model. Discrete & Continuous Dynamical Systems - A, 2009, 25 (2) : 651-667. doi: 10.3934/dcds.2009.25.651
[1]

Peng Zhang, Tong Zhang. The Riemann problem for scalar CJ-combustion model without convexity. Discrete & Continuous Dynamical Systems - A, 1995, 1 (2) : 195-206. doi: 10.3934/dcds.1995.1.195
[2]

Mauro Garavello, Francesca Marcellini. The Riemann Problem at a Junction for a Phase Transition Traffic Model. Discrete & Continuous Dynamical Systems - A, 2017, 37 (10) : 5191-5209. doi: 10.3934/dcds.2017225
[3]

Hermann Köenig, Vitali Milman. Derivative and entropy: the only derivations from $C^1(RR)$ to $C(RR)$. Electronic Research Announcements, 2011, 18: 54-60. doi: 10.3934/era.2011.18.54
[4]

Lakmi Niwanthi Wadippuli, Ivan Gudoshnikov, Oleg Makarenkov. Global asymptotic stability of nonconvex sweeping processes. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 0-0. doi: 10.3934/dcdsb.2019212
[5]

Darko Mitrovic. New entropy conditions for scalar conservation laws with discontinuous flux. Discrete & Continuous Dynamical Systems - A, 2011, 30 (4) : 1191-1210. doi: 10.3934/dcds.2011.30.1191
[6]

M. Zuhair Nashed, Alexandru Tamasan. Structural stability in a minimization problem and applications to conductivity imaging. Inverse Problems & Imaging, 2011, 5 (1) : 219-236. doi: 10.3934/ipi.2011.5.219
[7]

Angel Castro, Diego Córdoba, Charles Fefferman, Francisco Gancedo, Javier Gómez-Serrano. Structural stability for the splash singularities of the water waves problem. Discrete & Continuous Dynamical Systems - A, 2014, 34 (12) : 4997-5043. doi: 10.3934/dcds.2014.34.4997
[8]

Minhajul, T. Raja Sekhar, G. P. Raja Sekhar. Stability of solutions to the Riemann problem for a thin film model of a perfectly soluble anti-surfactant solution. Communications on Pure & Applied Analysis, 2019, 18 (6) : 3367-3386. doi: 10.3934/cpaa.2019152
[9]

Anupam Sen, T. Raja Sekhar. Structural stability of the Riemann solution for a strictly hyperbolic system of conservation laws with flux approximation. Communications on Pure & Applied Analysis, 2019, 18 (2) : 931-942. doi: 10.3934/cpaa.2019045
[10]

Michel Cristofol, Jimmy Garnier, François Hamel, Lionel Roques. Uniqueness from pointwise observations in a multi-parameter inverse problem. Communications on Pure & Applied Analysis, 2012, 11 (1) : 173-188. doi: 10.3934/cpaa.2012.11.173
[11]

Martin Gugat, Michael Herty, Siegfried Müller. Coupling conditions for the transition from supersonic to subsonic fluid states. Networks & Heterogeneous Media, 2017, 12 (3) : 371-380. doi: 10.3934/nhm.2017016
[12]

Konstantina Trivisa. Global existence and asymptotic analysis of solutions to a model for the dynamic combustion of compressible fluids. Conference Publications, 2003, 2003 (Special) : 852-863. doi: 10.3934/proc.2003.2003.852
[13]

Christophe Chalons. Theoretical and numerical aspects of the interfacial coupling: The scalar Riemann problem and an application to multiphase flows. Networks & Heterogeneous Media, 2010, 5 (3) : 507-524. doi: 10.3934/nhm.2010.5.507
[14]

Mauro Garavello. Boundary value problem for a phase transition model. Networks & Heterogeneous Media, 2016, 11 (1) : 89-105. doi: 10.3934/nhm.2016.11.89
[15]

Zhen-Hui Bu, Zhi-Cheng Wang. Global stability of V-shaped traveling fronts in combustion and degenerate monostable equations. Discrete & Continuous Dynamical Systems - A, 2018, 38 (5) : 2251-2286. doi: 10.3934/dcds.2018093
[16]

Jean Lerbet, Noël Challamel, François Nicot, Félix Darve. Kinematical structural stability. Discrete & Continuous Dynamical Systems - S, 2016, 9 (2) : 529-536. doi: 10.3934/dcdss.2016010
[17]

Stefano Bianchini, Elio Marconi. On the concentration of entropy for scalar conservation laws. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 73-88. doi: 10.3934/dcdss.2016.9.73
[18]

Igor Kossowski, Katarzyna Szymańska-Dębowska. Solutions to resonant boundary value problem with boundary conditions involving Riemann-Stieltjes integrals. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 275-281. doi: 10.3934/dcdsb.2018019
[19]

Francesca Marcellini. Existence of solutions to a boundary value problem for a phase transition traffic model. Networks & Heterogeneous Media, 2017, 12 (2) : 259-275. doi: 10.3934/nhm.2017011
[20]

Rafael Ortega, Andrés Rivera. Global bifurcations from the center of mass in the Sitnikov problem. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 719-732. doi: 10.3934/dcdsb.2010.14.719

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (9)
  • HTML views (0)
  • Cited by (9)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences