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In this note we discuss blow-up at space infinity for quasilinear
parabolic equation $u_t = \Delta u^m + u^{p}$. It is known that if
initial data is not a constant and takes its maximum at space
infinity in a certain sense, the solution blows up only at space
infinity at minimal blow-up time. We show that if $m \ge 1$ and a
solution blows up at minimal blow-up time, then it blows up
completely at the blow-up time.