Existence and upper semicontinuity of global attractors for a p-Laplacian inclusion

In this work we study the asymptotic behavior of a p-Laplacian in elusion of the form partial derivative u lambda/partial derivative t - div(D-lambda |del u(lambda)|(p-2)del u(lambda) + |u(lambda)|(p-2)u lambda is an element of F(u(lambda)) + h , where p > 2, h is an element of L-2 (Omega), with Omega subset of R-n,R- n >= 1,a bounded smooth domain, DA E infinity > M >= D-lambda (x) >= sigma > 0 a.e. in Omega, lambda is an element of[0, infinity) and D lambda -> D-lambda 1 in L infinity(Omega) as lambda ->lambda(1), F: D(F) subset of L-2 (Omega) -> P(L-2 (Omega)), given by F(y(center dot)0) = xi(center dot) is an element of L-2(Omega) : xi(x) is an element of f (y(x)) x-a.e. in Omega} with f : = R -> e(v) (R) a multiwilued Lipschitz map, where e(v)(R) is the set of all nonempty, bounded, closed, convex subsets of R. We prove the existence of a global attractor in L-2(Omega) for each positive finite diffusion coefficient and we show that the family of attractors behaves upper semicontinuously on positive finite diffusion parameters.