Inertial manifolds for nonautonomous dynamical systems and for nonautonomous evolution equations
Inertial manifolds for retarded second order in time evolution equations in admissible spaces
Using the Lyapunov-Perron method, we prove the existence of an inertial manifold for the process associated to a class of non-autonomous semilinear hyperbolic equations with finite delay, where the linear principal part is positive definite with a discrete spectrum having a sufficiently large distance between some two successive spectral points, and the Lipschitz coefficient of the nonlinear term may depend on time and belongs to some admissible function spaces.
Investigations of retarded PDEs of second order in time using the method of inertial manifolds with delay
Inertial manifold with delay (IMD) for dissipative systems of second order in time is constructed. This result is applied to the study of different asymptotic properties of solutions. Using IMD, we construct approximate inertial manifolds containing all the stationary solutions and give a new characterization of the K-invariant manifold.