Stability of strong detonation waves and rates of convergence
نویسنده
چکیده
In this article, we prove stability of strong detonation waves and find their rate of convergence for a combustion model. Our results read as follows: I) There exists a global solution that converges exponentially in time to a strong detonation wave, provided that the initial data is a small perturbation of a strong detonation wave that decays exponentially in |x|. II) When the initial perturbation decays algebraically in |x|, the solution converges algebraically in time. That is, the perturbation decays in t as ‘fast’ as the initial perturbation decays in |x|.
منابع مشابه
Viscous Hyperstabilization of Detonation Waves in One Space Dimension
It has long been a standard practice to neglect diffusive effects in stability analyses of detonation waves. Here, with the principal aim of quantifying the impact of these oft-neglected effects on the stability characteristics of such waves, we use numerical Evans-function techniques to study the (spectral) stability of viscous strong detonation waves—particular traveling-wave solutions of the...
متن کاملInitiation of subsonic detonation
The long-time behavior of the solution of the system θτ−απτ = Ω(θ), πτ−θτ = πξξ is investigated. Such a system is related to the modeling of detonation waves subjected to strong hydraulic resistance. We establish that some initial conditions yield decay (failure of ignition) while for other initial conditions our results strongly suggest convergence to traveling waves (successful ignition).
متن کاملStability of detonation profiles in the ZND limit
Confirming a conjecture of Lyng–Raoofi–Texier–Zumbrun, we show that stability of strong detonation waves in the ZND, or small-viscosity, limit is equivalent to stability of the limiting ZND detonation together with stability of the viscous profile associated with the component Neumann shock. More, on bounded frequencies the nonstable eigenvalues of the viscous detonation wave converge to those ...
متن کاملStability of cosmological detonation fronts.
We present results of a linear stability analysis of relativistic detonation fronts, which have been considered as representing phase interfaces in cosmological first order phase transitions. After discussing general stability conditions for detonation fronts, we concentrate on the properties of the fronts with respect to corrugation instabilities and discuss separately the cases of Chapman-Jou...
متن کاملLow Frequency Stability of Multi-dimensional Inviscid Planar Detonation Waves
We consider the problem of multi-dimensional linearized stability of planar, inviscid detonation waves. For an abstract, multi-step reaction model a normal mode analysis leads to a stability function similar to the Lopatinski determinant for gas dynamics. In the lowfrequency/long wave limit of the perturbation we obtain explicit criteria for uniform stability, weak stability, and strong instabi...
متن کامل