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

Wancheng Sheng; Tong Zhang

doi:10.3934/dcds.2009.25.651

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2009, Volume 25, Issue 2: 651-667. Doi: 10.3934/dcds.2009.25.651

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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
2.
Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100080

Received: December 31, 2007

Revised: January 31, 2009

Published: May 2009

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Abstract

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:

Scalar nonconvex C-J combustion model,
pointwise and global entropy conditions,
structural stability,
Riemann problem,
transition from deflagration to detonation.

Mathematics Subject Classification: 35L45, 35L60, 35L65, 35L67, 58J45, 76L05, 76N10, 80A25.

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