  We prove a local version of a (global) result of Merle and Zaag about ODE
behavior of solutions near blowup points for subcritical nonlinear heat
equations. As an application, for the equation $u_t= \Delta u+V(x)f(u)$, we
rule out the possibility of blowup at zero points of the potential $V$ for
monotone in time solutions when $f(u)\sim u^p$ for large $u$, both in the
Sobolev subcritical case and in the radial case. This solves a problem left
open in previous work on the subject. Suitable Liouville-type theorems play a
crucial role in the proofs.
