  The dust-acoustic waves and their stability in the permeating dusty plasma
with the Maxwellian velocity distribution are investigated. We derive the
dust-acoustic wave frequency and instability growth rate in two limiting
physical cases that the thermal velocity of the flowing dusty plasma is (a)
much larger than, and (b) much smaller than the phase velocity of the waves. We
find that the stability of the waves depend strongly on the velocity of the
flowing dusty plasma in the permeating dusty plasma. The numerical analyses are
made based on the example that a cometary plasma tail is passing through the
interplanetary space plasma. We show that, in case (a), the waves are generally
unstable for any flowing velocity, but in case (b), the waves become unstable
only when the wave number is small and the flowing velocity is large. When the
physical conditions are between these two limiting cases, we gain a strong
insight into the dependence of the stability criterions on the physical
conditions in the permeating dusty plasma.
