Robustness of global attractors of singularly perturbed plate equations

Abstract

In the paper, upper semicontinuity of global attractors of singularly perturbed plate equations on an unbounded domain with small positive parameter is considered. Under suitable assumptions, the equations possess a family of global attractors in natural energy space, and the corresponding singular limit equation, i.e. the parabolic equation, possesses a global attractor, which can be naturally embedded into a compact set of the natural energy space, and the upper semicontinuity of the family of global attractors to the compact set in the natural energy space (even more regular space) with respect to the Hausdorff semidistance, as the perturbation parameter tends to zero, was proved.