Different asymptotic behavior of global solutions for a parabolic system with nonlinear gradient terms

In this paper we study the global existence and the different asymptotic behavior of mild solutions for the nonlinear parabolic system: ∂tu=Δu+ap|∇v|, ∂tv=Δv+bq|∇u|, t>0, x∈RN, where a,b∈R, N⩾1, 1