Narrow Results

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.

In this paper we present an abstract approach to inertial manifolds for nonautonomous dynamical systems. Our result on the existence of inertial manifolds requires only two geometrical assumptions, called cone invariance and squeezing property, and two additional technical assumptions, called boundedness and coercivity property.