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On the One-dimensional Stability of Viscous Strong Detonation Waves
Building on Evans function techniques developed to study the stability of
viscous shocks, we examine the stability of viscous strong detonation wave
solutions of the reacting Navier-Stokes equations. The primary result,
following the work of Alexander, Gardner & Jones and Gardner & Zumbrun, is the
calculation of a stability index whose sign determines a necessary condition
for spectral stability. We show that for an ideal gas this index can be
evaluated in the ZND limit of vanishing dissipative effects. Moreover, when the
heat of reaction is sufficiently small, we prove that strong detonations are
spectrally stable provided the underlying shock is stable. Finally, for
completeness, the stability index calculations for the nonreacting
Navier-Stokes equations are includedComment: 66 pages, 7 figure