American Institute of Mathematical Sciences

Advanced
April  1995, 1(2): 195-206. doi: 10.3934/dcds.1995.1.195

The Riemann problem for scalar CJ-combustion model without convexity

Peng Zhang 1, and  Tong Zhang 2,

1. 

Institute of Mathematics, Academia Sinica, Beijing 100080, China
2. 

Institute of Mathematics, Academia Sinica, Beijing, 100080, China

Received  October 1994 Published  February 1995

The Riemann problem for scalar Chapman-Jouguet combustion model is considered. The entropy conditions are extended from convex case to nonconvex one. The existence and uniqueness of the corresponding entropy solutions are obtained constructively.The solutions consist of the generalized Chapman-Jouguet detonation and deflagration waves and strong detonation waves as well as noncombustion waves.
Keywords: nonconvexity., deflagration, combustion model detonation, Riemann problem.
Mathematics Subject Classification: 35L65, 76N1.
Citation: Peng Zhang, Tong Zhang. The Riemann problem for scalar CJ-combustion model without convexity. Discrete and Continuous Dynamical Systems, 1995, 1 (2) : 195-206. doi: 10.3934/dcds.1995.1.195
[1]

Wancheng Sheng, Tong Zhang. Structural stability of solutions to the Riemann problem for a scalar nonconvex CJ combustion model. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 651-667. doi: 10.3934/dcds.2009.25.651
[2]

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

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 and Applied Analysis, 2019, 18 (6) : 3367-3386. doi: 10.3934/cpaa.2019152
[4]

Yanbo Hu, Wancheng Sheng. The Riemann problem of conservation laws in magnetogasdynamics. Communications on Pure and Applied Analysis, 2013, 12 (2) : 755-769. doi: 10.3934/cpaa.2013.12.755
[5]

Rinaldo M. Colombo, Mauro Garavello. A Well Posed Riemann Problem for the $p$--System at a Junction. Networks and Heterogeneous Media, 2006, 1 (3) : 495-511. doi: 10.3934/nhm.2006.1.495
[6]

Vladimir S. Gerdjikov, Rossen I. Ivanov, Aleksander A. Stefanov. Riemann-Hilbert problem, integrability and reductions. Journal of Geometric Mechanics, 2019, 11 (2) : 167-185. doi: 10.3934/jgm.2019009
[7]

Meixiang Huang, Zhi-Qiang Shao. Riemann problem for the relativistic generalized Chaplygin Euler equations. Communications on Pure and Applied Analysis, 2016, 15 (1) : 127-138. doi: 10.3934/cpaa.2016.15.127
[8]

Constantine M. Dafermos. A variational approach to the Riemann problem for hyperbolic conservation laws. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 185-195. doi: 10.3934/dcds.2009.23.185
[9]

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
[10]

Michael L. Frankel, Victor Roytburd. Dynamical structure of one-phase model of solid combustion. Conference Publications, 2005, 2005 (Special) : 287-296. doi: 10.3934/proc.2005.2005.287
[11]

Claude-Michel Brauner, Josephus Hulshof, Luca Lorenzi, Gregory I. Sivashinsky. A fully nonlinear equation for the flame front in a quasi-steady combustion model. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 1415-1446. doi: 10.3934/dcds.2010.27.1415
[12]

Josephus Hulshof, Pascal Noble. Travelling waves for a combustion model coupled with hyperbolic radiation moment models. Discrete and Continuous Dynamical Systems - B, 2008, 10 (1) : 73-90. doi: 10.3934/dcdsb.2008.10.73
[13]

Claude-Michael Brauner, Josephus Hulshof, J.-F. Ripoll. Existence of travelling wave solutions in a combustion-radiation model. Discrete and Continuous Dynamical Systems - B, 2001, 1 (2) : 193-208. doi: 10.3934/dcdsb.2001.1.193
[14]

Fiammetta Conforto, Maria Groppi, Roberto Monaco, Giampiero Spiga. Kinetic approach to deflagration processes in a recombination reaction. Kinetic and Related Models, 2011, 4 (1) : 259-276. doi: 10.3934/krm.2011.4.259
[15]

Lihui Guo, Wancheng Sheng, Tong Zhang. The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system$^*$. Communications on Pure and Applied Analysis, 2010, 9 (2) : 431-458. doi: 10.3934/cpaa.2010.9.431
[16]

João-Paulo Dias, Mário Figueira. On the Riemann problem for some discontinuous systems of conservation laws describing phase transitions. Communications on Pure and Applied Analysis, 2004, 3 (1) : 53-58. doi: 10.3934/cpaa.2004.3.53
[17]

Chun Shen, Wancheng Sheng, Meina Sun. The asymptotic limits of solutions to the Riemann problem for the scaled Leroux system. Communications on Pure and Applied Analysis, 2018, 17 (2) : 391-411. doi: 10.3934/cpaa.2018022
[18]

Gui-Qiang G. Chen, Qin Wang, Shengguo Zhu. Global solutions of a two-dimensional Riemann problem for the pressure gradient system. Communications on Pure and Applied Analysis, 2021, 20 (7&8) : 2475-2503. doi: 10.3934/cpaa.2021014
[19]

Tong Li, Nitesh Mathur. Riemann problem for a non-strictly hyperbolic system in chemotaxis. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 2173-2187. doi: 10.3934/dcdsb.2021128
[20]

Kuo-Chih Hung, Shin-Hwa Wang. Classification and evolution of bifurcation curves for a porous-medium combustion problem with large activation energy. Communications on Pure and Applied Analysis, 2021, 20 (2) : 559-582. doi: 10.3934/cpaa.2020281

2021 Impact Factor: 1.588

Tools

Metrics

  • PDF downloads (93)
  • HTML views (0)
  • Cited by (10)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy