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We classify the self-similar blow-up profiles for the followingreaction-diffusion equation with critical strong weighted reaction andunbounded weight: $$ \partial_tu=\partial_{xx}(u^m) + |x|^{\sigma}u^p, $$ posedfor $x\in\real$, $t\geq0$, where $m>1$, $0<p<1$ such that $m+p=2$ and$\sigma>2$ completing the analysis performed in a recent work where this veryinteresting critical case was left aside. We show that finite time blow-upsolutions in self-similar form exist for $\sigma>2$. Moreover all the blow-upprofiles have compact support and their supports are \emph{localized}: thereexists an explicit $\eta>0$ such that any blow-up profile satisfies ${\rmsupp}\,f\subseteq[0,\eta]$. This property is unexpected and contrasting withthe range $m+p>2$. We also classify the possible behaviors of the profiles nearthe origin.

Self-similar blow-up profiles for a reaction-diffusion equation with critically strong weighted reaction