## Inertial manifolds for retarded second order in time evolution equations in admissible spaces

### Volume 108 / 2013

Annales Polonici Mathematici 108 (2013), 21-42
MSC: Primary 35B40; Secondary 35B42, 49K25, 35K55, 34C30.
DOI: 10.4064/ap108-1-3

#### Abstract

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.