Weak singularity dynamics in a nonlinear viscous medium

Abstract

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.