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 strong-detonation-wave solutions of the Navier-Stokes equations for reacting gas. The primary result, following [1, 17], 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 Zeldovich-von Neumann-Döring limit of vanishing dissipative effects. Moreover, when the heat of reaction is sufficiently small, we prove that strong detonations are spectrally stable provided that the underlying shock is stable. Finally, for completeness, we include the calculation of the stability index for a viscous shock solution of the Navier-Stokes equations for a nonreacting gas.

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Recommended citation: Gregory Lyng & Kevin Zumbrun, One-dimensional stability of viscous strong detonation waves. Archive for Rational Mechanics and Analysis, 173 (2004): 213–277.