Extinction properties of solutions for a class of fast diffusive pp-Laplacian equations

We consider the extinction properties of solutions for the homogeneous Dirichlet boundary value problem for the pp-Laplacian equation ut−div(∣∇u∣p−2∇u)+βuq=λur with 10r,λ,β>0. For β=0β=0, it is known that r=p−1r=p−1 is the critical extinction exponent for the weak solution. For β>0β>0, we show that r=p−1r=p−1 is still the critical extinction exponent when q=1q=1. Moreover, the precise decay estimates of solutions before the occurrence of the extinction are derived. However, extinction can always occur when 0