2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219204We study the long time behaviour of solutions of semi-linear parabolic equation of the following type $\partial_t u-Δu+a_0(x)u^q=0$ where $a_0(x) \geq d_0 \exp(\frac{ω(|x|)}{|x|^2})$, $d_0>0$, $1>q>0$ and $ω$ a positive continuous radial function. We give a Dini-like condition on the function $ω$ by two different method which implies that any solution of the above equation vanishes in a finite time. The first one is a variant of a local energy method and the second one is derived from semi-classical limits of some Schrödinger operators.Analysis of PDEs35B40, 35K20, 35P15text