Global Attractors For A Weighted P(x)-Laplacian Evolution Equation With Degeneracy

In this paper, the long-time behavior for a class of weighted p(x)-Laplacian evolution equations will be considered in a bounded domain Ω, where the diffusion coefficient ω is a given nonnegative measurable and finite function a.e.in Ω,ω(x)=0 on the closed subset Ω0 of Ω with zero measure, the nonlinearity f satisfies a polynomial growth of arbitrary order. Firstly, the global existence and uniqueness of weak solution will be shown in variable exponent spaces using approximating degenerate prob-lems by non-degenerate ones; Secondly, we prove the existence of absorbing sets in Lq(x)(Ω)(q(x)≤2) and W01 (ω,Ω), and obtain the existence of global attractor in L2(Ω) using the method of uniform compactness; Finally, we verify the semigroup associated with our problem is asymptotically compact in Lq(x) (Ω) and W01 (ω,Ω) using the asymptotic a priori estimate. And then the existence of global attractors in Lq(x)(Ω) and W01,p(x)(ω,Ω) are shown, respectively.