The nonstationary problem of the evolution of perturbation and its transfor
mation into nonlinear wave structure in complex plasmas (multicomponent pla
smas containing ions, electrons, charged microspheres or dust grains, and n
eutral gas) is considered. For this purpose, the model, which takes into ac
count the variation of ion density and the ion-momentum dissipation due to
dust-particle charging, as well as the source of plasma particles due to th
e ionization process, is developed. The model is appropriate for the descri
ption of laboratory experiments in complex plasmas and contains all basic m
echanisms responsible for the formation of a new kind of shock waves which
is related to the anomalous dissipation due to the dust-particle charging p
rocess. The consideration on the basis of this model allows us to obtain sh
ock structures as a result of evolution of an initial perturbation and to e
xplain the experimental value of the width of the ion acoustic shock-wave f
ront, as well as the shock-wave speed. The solution of the problem of the e
volution of perturbation and its transformation into a shock wave in comple
x plasmas opens up possibilities for description of the real phenomena like
supernova explosions, as well as of the laboratory and active space and ge
ophysical experiments. (C) 2001 MAIK "Nauka/Interperiodica".