We study the property of extinction in a finite time for nonnegative solutions of 1/q ∂t (u q) − delta_p u + a(x)u^λ = 0 for the Dirichlet Boundary Conditions when q > λ > 0, p ≥ 1 + q, p ≥ 2, a(x) ≥ 0 and Ω ⊂ R^N a bounded domain of R^N (N ≥ 1). Necessary and sufficient conditions are provided with the help of a family of infimum. When p > 1 + q, the threshold is for power functions but for p = 1 + q, it happens extinction in a finite time for very flat functions.