Cone invariance and squeezing properties for inertial manifolds for nonautonomous evolution equations

@article{NorbertKoksch2003,
abstract = {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.},
author = {Norbert Koksch, Stefan Siegmund},
journal = {Banach Center Publications},
keywords = {nonautonomous dynamical systems; nonautonomous evolution equations; inertial manifolds; Lyapunov-Perron method; Hadamard method; spectral gap condition; cone invariance property; squeezing property; dichotomy},
language = {eng},
number = {1},
pages = {27-48},
title = {Cone invariance and squeezing properties for inertial manifolds for nonautonomous evolution equations},
url = {http://eudml.org/doc/281828},
volume = {60},
year = {2003},
}

TY - JOUR
AU - Norbert Koksch
AU - Stefan Siegmund
TI - Cone invariance and squeezing properties for inertial manifolds for nonautonomous evolution equations
JO - Banach Center Publications
PY - 2003
VL - 60
IS - 1
SP - 27
EP - 48
AB - 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.
LA - eng
KW - nonautonomous dynamical systems; nonautonomous evolution equations; inertial manifolds; Lyapunov-Perron method; Hadamard method; spectral gap condition; cone invariance property; squeezing property; dichotomy
UR - http://eudml.org/doc/281828
ER -