In this paper we summarize 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 some additional technical assumptions like boundedness or smoothing properties. We apply this result to processes (two-parameter semiflows) generated by nonautonomous semilinear parabolic evolution equations.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc60-0-2,
author = {Norbert Koksch and Stefan Siegmund},
title = {Cone invariance and squeezing properties for inertial manifolds for nonautonomous evolution equations},
journal = {Banach Center Publications},
volume = {60},
year = {2003},
pages = {27-48},
zbl = {1037.34039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc60-0-2}
}
Norbert Koksch; Stefan Siegmund. Cone invariance and squeezing properties for inertial manifolds for nonautonomous evolution equations. Banach Center Publications, Tome 60 (2003) pp. 27-48. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc60-0-2/