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For strong detonation waves of the inviscid Majda model, spectral stability was established by Jung and Yao for waves with step-type ignition functions, by a proof based largely on explicit knowledge of wave profiles. In the present work, we extend their stability results to strong detonation waves with more general ignition functions where explicit profiles are unknown. Our proof is based on reduction to a generalized Sturm-Liouville problem, similar to that used by Sukhtayev, Yang, and Zumbrun to study spectral stability of hydraulic shock profiles of the Saint-Venant equations.
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Recent results on stability of planar detonations.
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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- Award ID(s):
- 1700279
- PAR ID:
- 10057694
- Date Published:
- Journal Name:
- Shocks, singularities and oscillations in nonlinear optics and fluid mechanics
- Volume:
- 17
- Page Range / eLocation ID:
- 273-308
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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- The DOI is not currently available.
