Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Stability of ZND detonations for Majda's model


Authors: Soyeun Jung and Jinghua Yao
Journal: Quart. Appl. Math. 70 (2012), 69-76
MSC (2000): Primary 76L05; Secondary 76E99, 76N99, 80A32
DOI: https://doi.org/10.1090/S0033-569X-2011-01232-3
Published electronically: August 26, 2011
MathSciNet review: 2920616
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Abstract: We evaluate by direct calculation the Lopatinski determinant for ZND detonations in Majda's model for reacting flow and show that on the nonstable (nonnegative real part) complex half-plane it has a single zero at the origin of multiplicity one, implying stability. Together with results of Zumbrun on the inviscid limit, this recovers the result of Roquejoffre-Vila that viscous detonations of Majda's model also are stable for sufficiently small viscosity, for any fixed detonation strength, heat release, and rate of reaction.


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Additional Information

Soyeun Jung
Affiliation: Indiana University, Bloomington, Indiana 47405
Email: soyjung@indiana.edu

Jinghua Yao
Affiliation: Indiana University, Bloomington, Indiana 47405
Email: yaoj@indiana.edu

DOI: https://doi.org/10.1090/S0033-569X-2011-01232-3
Received by editor(s): May 21, 2010
Published electronically: August 26, 2011
Additional Notes: The research of S.J. and J.Y. was partially supported under NSF grants number DMS-0070765 and DMS-0300487. Thanks to Kevin Zumbrun for suggesting the problem and for helpful discussions.
Article copyright: © Copyright 2011 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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