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Erschienen in:
Amplitude Equations for Weakly Nonlinear Surface Waves in Variational Problems Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

Recent Results on Stability of Planar Detonations

verfasst von : Kevin Zumbrun

Erschienen in: Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics

Verlag: Springer International Publishing

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Abstract

We describe recent analytical and numerical results on stability and behavior of viscous and inviscid detonation waves obtained by dynamical systems/Evans function techniques like those used to study shock and reaction diffusion waves. In the first part, we give a broad description of viscous and inviscid results for 1D perturbations; in the second, we focus on inviscid high-frequency stability in multi-D and associated questions in turning point theory/WKB expansion.

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Vorheriges Kapitel Geometric Optics for Rayleigh Pulses in Nonlinear Elasticity
Fußnoten
1
Condition [44, (5.13)] comparing relative sizes of oscillatory modes in the first-order expansion of decaying solution \(\tilde{Z}\), depending on the geometry of background profile \(\bar{W}\); see [44, Prop. 5.1] and discussion just below.
 
2
As discussed in [45], Erpenbeck treated turning points/glancing modes at points x ∗ bounded away from 0 and ∞; however, these cases necessarily occur at certain boundary frequencies, so must be considered in a complete stability analysis, as must be issues not treated in [22] of uniformity for frequencies near but not at a glancing point.
 
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Metadaten
Titel
Recent Results on Stability of Planar Detonations
verfasst von
Kevin Zumbrun
Copyright-Jahr
2017
Buch
Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics

Print ISBN: 978-3-319-52041-4

Electronic ISBN: 978-3-319-52042-1

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-52042-1_11