  The existence and structure of steady gaseous detonation propagating in a
packed bed of solid inert particles are analyzed in the one-dimensional
approximation by taking into consideration frictional and heat losses between
the gas and the particles. A new formulation of the governing equations is
introduced that eliminates the well-known difficulties with numerical
integration across the sonic singularity in the reactive Euler equations. The
new algorithm allows us to determine that the detonation solutions as the loss
factors are varied have a set-valued nature at low detonation velocities when
the sonic constraint disappears from the solutions. These set-valued solutions
correspond to a continuous spectrum of the eigenvalue problem that determines
the velocity of the detonation.
