Stability of Viscous Weak Detonation Waves for Majda’s Model

  • Jeffrey Hendricks
  • Jeffrey Humpherys
  • Gregory Lyng
  • Kevin Zumbrun


Continuing the program initiated by Humpherys et al. (Physica D 259:63–80, 2013) for strong detonation waves, we use a combination of analytical and numerical Evans-function techniques to analyze the spectral stability of weak detonation waves in a simplified model for gas-dynamical combustion. Combining these new spectral stability results with the pointwise Green function analysis of Lyng et al. (J Differ Equ 233(2):654–698, 2007), we conclude that these waves are nonlinearly stable. The principal novelty of this analysis is the treatment of weak detonation waves. In contrast to the case of strong detonation waves, weak detonation waves are under compressive and the stability of these waves is delicate and has not been treated by standard weighted-norm techniques. The present analysis thus provides a case study illustrating the flexibility and power of the Evans-function-based approach to stability. As in the case of strong detonations, we find that all tested waves are spectrally stable, hence nonlinearly stable.


Stability Detonations Evans function Combustion Majda model 



Humpherys was partially supported by NSF Grant DMS-0847074 (CAREER). Lyng was partially supported by NSF Grant DMS-0845127 (CAREER). Zumbrun was partially supported by NSF Grant DMS-0801745.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Jeffrey Hendricks
    • 1
  • Jeffrey Humpherys
    • 1
  • Gregory Lyng
    • 2
  • Kevin Zumbrun
    • 3
  1. 1.Department of MathematicsBrigham Young UniversityProvoUSA
  2. 2.Department of MathematicsUniversity of WyomingLaramieUSA
  3. 3.Department of MathematicsIndiana UniversityBloomingtonUSA

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