ABSTRACT
This chapter presents a result concerning the nonexistence of inertial manifolds for the semiflow generated by a semi-linear dissipative wave equation. It discusses the perturbation of the nonlinear flow generated by a nonlinear problem showing that, on one hand, the long-time behavior of the perturbed flow is the same as that of nonlinear flow in a neighborhood of its stationary state, and, on the other, the global attractor of the perturbed flow, which must coincide with the global attractor, is not contained in any of the manifolds. The chapter also proves the linearization equivalence theorems for a single operator and groups of operators.
