This paper deals with the large time behavior of nonnegative solutions to the equation $$u_t = div\left( {\left| {\nabla u} \right|^{p - 2} \nabla u} \right) + a\left( x \right)u^q ,\left( {x,t} \right) \in R^N \times (0,T),$$ where p > 2, q > 0, and the function a(x) ≥ 0 has a compact support. We obtain the critical exponent for global existence q 0 and the Fujita exponent q c . In one-dimensional case N = 1, we have $$q_0 = \frac{{2(p - 1)}} {p}$$ and q c = 2(p − 1). Particularly, all solutions are global in time if 0 < q ≤ q o, but blow up if q 0 < q ≤ q c ; while if q > q c both blowing up solutions and global solutions exist. However, for the case N ≥ p > 2, these two critical exponents are exactly the same. Namely, q 0 = p − 1 = q c .