Existence and upper semicontinuity of global attractors for p(x)-Laplacian systems

This work concerns the study of asymptotic behavior of coupled systems of p(x)-Laplacian differential inclusions. We obtain that the generalized semiflow generated by the coupled system has a global attractor for each pair of positive diffusion coefficients. We also prove that the attractors are upper semicontinuous on positive finite diffusion parameters. In particular, to get the results we prove that the p(x)-Laplacian operator is subdifferential of a convex, proper and lower semicontinuous non-negative map.