We consider the equation psi t - Delta psi + c vertical bar psi vertical bar (p-1)psi = 0 with Neumann boundary conditions in a bounded smooth open connected domain of R-n with p > 1, c > 0. We show that if the initial condition is small enough and if the absolute value of its average overpasses a certain multiple of the pth power of its L-infinity norm, then psi(t, .) decreases like t(-1/(p-1)).