  In this paper we investigate the propagation of singularities in a nonlinear
parabolic equation with strong absorption when the absorption potential is
strongly degenerate following some curve in the $(x,t)$ space. As a very
simplified model, we assume that the heat conduction is constant but the
absorption of the media depends stronly of the characteristic of the media.
More precisely we suppose that the temperature $u$ is governed by the following
equation \label{I-1} \partial_{t}u-\Delta u+h(x,t)u^p=0\quad
\text{in}Q_{T}:=R^N\times (0,T) where $p>1$ and $h\in C(\bar Q_{T})$. We
suppose that $h(x,t)>0$ except when $(x,t)$ belongs to some space-time curve.
