  We derive and study equations for dissipative transient processes in a
constraint incommensurate charge density wave (CDW) with remnant pockets or a
thermal population of normal carriers. The attention was paid to give the
correct conservation of condensed and normal electrons, which was problematic
at presence of moving dislocation cores if working within an intuitive
Ginzburg-Landau like model. We performed a numeric modelling for stationary and
transient states in a rectangular geometry when the voltage V or the normal
current are applied across the conducting chains. We observe creation of an
array of electronic vortices, the dislocations, at or close to the junction
surface; their number increases stepwise with increasing V. The dislocation
core strongly concentrates the normal carriers but the CDW phase distortions
almost neutralize the total charge. At other regimes, the lines of the zero CDW
amplitude flash across the sample working as phase slips. The studies were
inspired by, and can be applied to experiments on mesa-junctions in NbSe3 and
TaS3 (Yu.I. Latyshev et al in proceedings of ECRYS 2008 and 2011).
