Initial-value problem for small disturbances in an idealized one-dimensional detonation

The solution of the initial-value problem for linearized reactive Euler equations is presented as an expansion into modes of discrete and continuous spectra in the case of one-dimensional perturbations. The result provides a convenient tool to predict initial amplitudes of the unstable modes depending on the initial perturbation. Examples of initial perturbations introduced into the quiescent gas and into the reaction zone are discussed. It is shown that the discrete spectrum stemming from the solution of the initial-value problem for an idealized one-reaction detonation is equivalent to the spectrum of the conventional normal-mode approach.