Excluding blowup at zero points of the potential by means of Liouville-type theorems

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 ut=Δu+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)∼up 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.