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

In this paper, we investigate the behavior of the positive solution of the following Cauchy problemut−div(|∇um|p−2∇um)=uqut−div(|∇um|p−2∇um)=uq with initial value decaying at infinity, and give a new secondary critical exponent for the existence of global and nonglobal solutions. Furthermore, the large time behavior and the life span of solutions are also studied.