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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap108-1-3,
author = {Cung The Anh and Le Van Hieu},
title = {Inertial manifolds for retarded second order in time evolution equations in admissible spaces},
journal = {Annales Polonici Mathematici},
volume = {107},
year = {2013},
pages = {21-42},
zbl = {1263.35045},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap108-1-3}
}
Cung The Anh; Le Van Hieu. Inertial manifolds for retarded second order in time evolution equations in admissible spaces. Annales Polonici Mathematici, Tome 107 (2013) pp. 21-42. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap108-1-3/