Energy non-collapsing and refined blowup for a semilinear heat equation

Refined structures of blowup for non-collapsing maximal solution to a semilinear parabolic equation

$u_t?△u=|u{|}^{p?1}u$

with $p>1$ are studied. We will prove that the blowup set is empty for non-collapsing blowing-up in subcritical case, and all finite time non-collapsing blowing-up must be refined type II in critical case. When $p>p_S\equiv \frac{N+2}{N?2}$ for $N\ge 3$, the Hausdorff dimension of the blowup set for maximal solution whose energy is non-collapsing is shown to be no greater than $N?2?\frac{4}{p?1}$, which answers a question proposed in [7] positively. At the end of this paper, we also present some new examples of collapsing and non-collapsing blowups.