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| Perturbed Riemann Problem for a ScalarChapman-Jouguet Combustion Model |
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Citation： |
Meina SUN1.Perturbed Riemann Problem for a ScalarChapman-Jouguet Combustion Model[J].Chinese Annals of Mathematics B,2015,36(2):267~278 |
| Page view： 2394
Net amount： 1602 |
Authors： |
Meina SUN1; |
Foundation： |
the National Natural Science Foundation of China (No. 11271176) and
the Shandong Provincial Higher Educational Science and Technology Program (No. J12LI01). |
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| Abstract： |
The author considers the perturbed Riemann problem for a scalar Chapman-
Jouguet combustion model which comes from Majda’s model with a modified, bump-type
ignition function proposed in the results of Lyng and Zumbrun in 2004. Under the entropy
conditions, the unique solution in a neighborhood of the origin on the (x, t) plane (t > 0) is
obtained. It is found that, for some cases, the perturbed Riemann solutions are essentially
different from the corresponding Riemann solutions. The perturbation may transform a
strong detonation into a weak deflagration in the neighborhood of the origin. Especially, it
can be observed that burning happens although the corresponding Riemann solution does
not contain combustion wave, which exhibits the instability for the unburnt state. |
Keywords： |
Scalar Chapman-Jouguet combustion model, Perturbed Riemann problem,
Detonation, Deflagration |
Classification： |
35L65, 35L67, 76N15 |
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