Life span and a new critical exponent for a quasilinear degenerate parabolic equation with slow decay initial values

In this paper, we consider the positive solution of a Cauchy problem for the following PP-Laplace parabolic equation ut=div(|∇u|p−2∇u)+uq,p>2,q>1, and give a secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence of global and nonglobal solutions of the Cauchy problem. Furthermore, the life span of solutions is also studied.