  We consider a system of nonlinear equations which can be reduced to a
degenerate parabolic equation. In the case $x\in\bR^2$ we obtained necessary
conditions for the existence of a weakly singular solution of heat wave type
($\codim\sing\supp=1$) and of vortex type ($\codim\sing\supp=2$). These
conditions have the form of a sequence of differential equations and allow one
to calculate the dynamics of the singularity support. In contrast to the
methods used traditionally for degenerate parabolic equations, our approach is
not based on comparison theorems.
