Abstract
Inertial manifolds for a class of second order in time dissipative equations are constructed. The author also proves an asymptotic completeness property for the inertial manifolds and characterizes the inertial manifolds as the set of trajectories whose growth is at most of order O(e-μt) for some μ > 0. As applications, a nonlinear wave equation and a problem of nonlinear oscillations of a shallow shell are considered.
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