LAUSR

In this paper, we mainly consider the initial boundary problem for a quasilinear parabolic equation $${u_t} - div\left( {{{\left| {\nabla u} \right|}^{p - 2}}\nabla u} \right) = - {\left| u \right|^{\beta - 1}}u + \alpha {\left| u \right|^{q - 2}}u,$$ut−div(|∇u|p−2∇u)=−|u|β−1u+α|u|q−2u, where p > 1; β > 0, q ≥ 1 and α > 0. By using Gagliardo-Nirenberg type inequality, the energy method and comparison principle, the phenomena of blowup and extinction are classified completely in the different ranges of reaction exponents.