The perturbation on initial binding energy for a Majda-CJ combustion model

Abstract

We investigate the perturbed Riemann problem for a scalar Chapman–Jouguet combustion model – the perturbation on initial binding energy. Under the entropy conditions, we obtain the unique solutions in a neighbourhood of the origin (t > 0) on the (x, t) plane. It is found that, for some cases, the perturbed Riemann solutions are essentially different from the corresponding Riemann solutions. That is, the perturbation may transform a Chapman–Jouguet detonation into a strong detonation or a weak deflagration following a shock wave; a strong detonation into a weak deflagration following a shock wave; a Chapman–Jouguet deflagration into a weak deflagration.

Keywords:

• Majda-CJ combustion model
• perturbation of binding energy
• detonation
• deflagration

AMS Subject Classifications::

• 35L65
• 35L67
• 76N15

Acknowledgements

The authors are grateful to the anonymous referees for their valuable comments which improve the presentation of the paper greatly. This research is supported in part by the National Natural Science Foundation of China (11271176, 11001116, 10901077), the Project of Shandong Provincial Higher Educational Science and Technology Program (J11LA03, J12LI01), Shandong Provincial Natural Science Foundation (ZR2010AL012) and Shandong Provincial Doctoral Foundation (BS2010SF006).