  If $\Omega$ is a bounded domain in $\mathbb R^N$ and $f$ a continuous
increasing function satisfying a super linear growth condition at infinity, we
study the existence and uniqueness of solutions for the problem (P):
$\partial_tu-\Delta u+f(u)=0$ in $Q_\infty^\Omega:=\Omega\times (0,\infty)$,
$u=\infty$ on the parabolic boundary $\partial_{p}Q$. We prove that in most
cases, the existence and uniqueness is reduced to the same property for the
associated stationary equation in $\Omega$.
