Stability of Converging Cylindrical Detonation

Converging cylindrical shocks in ideal magnetohydrodynamics

Stability 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...

Numerical predictions of oblique detonation stability boundaries

Oblique detonation stability was studied by numerically integrating the two-dimensional. one-step reactive Euler equations in a generalized, curvilinear coordinate system. The integration was accomplished using the Roe scheme combined with fractional stepping; nonlinear flux limiting was used to prevent unphysical solution oscillations near discontinuities. The method was verified on oneand two...

Optimization, Stability and Cylindrical Decomposition

Some connections between constructive real algebraic geometry and constrained optimization are exploited. We show how the problem of determining the projection of a real-algebraic variety on a certain axis is equivalent to a problem in nonlinear programming. As an application, Grr obner bases are used to deal with an optimization problem arising in the theory of local Lyapunov functions. The pr...

Stability of strong detonation waves and rates of convergence

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 perturba...