Upper Semicontinuity of Global Attractors for 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. Using the idea of tail estimates, the author established 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. The results obtained are new and are not common in the existing literature.