  The steady state propagation of a phase transition front is classified,
according to hydrodynamics, as a deflagration or a detonation, depending on its
velocity with respect to the fluid. These propagation modes are further divided
into three types, namely, weak, Jouguet, and strong solutions, according to
their disturbance of the fluid. However, some of these hydrodynamic modes will
not be realized in a phase transition. One particular cause is the presence of
instabilities. In this work we study the linear stability of weak detonations,
which are generally believed to be stable. After discussing in detail the weak
detonation solution, we consider small perturbations of the interface and the
fluid configuration. When the balance between the driving and friction forces
is taken into account, it turns out that there are actually two different kinds
of weak detonations, which behave very differently as functions of the
parameters. We show that the branch of stronger weak detonations are unstable,
except very close to the Jouguet point, where our approach breaks down.
