Second critical exponent for evolution pp-Laplacian equation with weighted source

This paper studies the Cauchy problem for the evolution pp-Laplacian equation with weighted source: ut=div(|∇u|p−2∇u)+|x|muqut=div(|∇u|p−2∇u)+|x|muq in Rn×(0,T)Rn×(0,T), where 2n/(n+1)n(2−p)−pm>n(2−p)−p, q>1q>1. We obtain the second critical exponent on decay orders of initial data at infinity to identify global and non-global solutions in the coexistence region of the two kinds of solutions. In addition, we determine the life span of the non-global solutions in the case of m=0m=0.