A Damped Hyperbolic Equation on Thin Domains
Jack K. Hale, Geneviève Raugel · Transactions of the American Mathematical Society · 1992
For a damped hyperbolic equation in a thin domain in ${{\mathbf {R}}^3}$ over a bounded smooth domain in ${{\mathbf {R}}^2}$, it is proved that the global attractors are upper semicontinuous. It is shown also that a global attractor exists in the case of the critical Sobolev exponent.