A note on maximal solutions of nonlinear parabolic equations with absorption

If $Ω$ 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): $\partial_tu-Δu+f(u)=0$ in $Q_\infty^Ω:=Ω\times (0,\infty)$, $u=\infty$ 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 $Ω$.

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