We consider the scalar parabolic equation $$ \left( 1 \right)_\varepsilon \left\{ {\begin{array}{*{20}c} {u_t = \Delta u - ku + b\left( {x,u} \right)\quad in\quad D_\varepsilon } \\ {\frac{{\partial u}} {{\partial n}} = 0\quad on\quad \partial D_\varepsilon } \\ \end{array} } \right. $$ where k > 0 is fixed, b: Rn × R → R is smooth, for some constant M we have |b(x,u)| < M, |bu(x,u)| < M for all (x,u)∈ Rn × R, and {De} is a family of open smooth domains in Rn such that for 0 ≤ e ≤ e' ≤ 1, De is contained in De', and |De−De'| → 0 as e → e'+, where |.| denotes the Lebesgue measure in Rn. We assume also that each De is connected and there is a ball B in Rn which contains every De.