2002, Vol.5, No.1, pp.21-32
We consider a system of nonlinear equations which can
be reduced to a degenerate parabolic equation. In the case
x in R2 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.
Key words:
degenerate parabolic equations, singularities, heat
wave, vortex
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