Existence And Upper Semicontinuity Of Attractors For Weighted P-Laplacian Systems

In this paper,we consider the long-time behavior of the solutions of the weighted p-Laplacian evolution equations(?)satisfying Dirichlet boundary condition in a bounded domain.On the one hand,when the external force term g is related to time,we assume that the nonlinearity term f satisfies the polynomial growth of arbitrary order,and the reaction-diffusion coefficient σ ∈C(Ω)and a(x)=0 for x ∈ F,σ(x)>0 for x ∈ Ω\F,where F is a closed subset of Ω with meas(F)=0.Futhermore,σ(x)satifies∫{x(?)Ω,}|x-x0|<r}1/[σ(x)n/x]dx<∞we discuss the existence of the pullback attractor of the nonautonomous system generated by the above weighted p-Laplacian evolution equation in L2(Ω)and Lq(Ω),furthermore,we discuss the upper semi-continuity of the pullback attractor.On the other hand,when the external force term g is independent of time,we assume that the nonlinearity term f satisfies the polynomial growth of arbitrary order,and the reaction-diffusion coefficient a satisfies the following assumption(Hσ)σ(x)∈Lloc1(Ω)and for some α ∈(0,p),liminfx→z|-ασ(x)>0,for every z∈Ω.we prove the upper semi-continuity of the global attractor of the autonomous system generated by the above weighted p-Laplacian evolution equation on the basis of[25].