American Institute of Mathematical Sciences

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