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 ? ?C(?)and a(x)=0 for x ? F,?(x)>0 for x ? ?\F,where F is a closed subset of ? with meas(F)=0.Futhermore,?(x)satifies?{x(?)?,}|x-x0|<r}1/[?(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(?)and Lq(?),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(H?)?(x)?Lloc1(?)and for some ? ?(0,p),liminfx?z|-??(x)>0,for every z??.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].