Almost sharp conditions for the existence of smooth inertial manifolds
Inertial manifolds for nonautonomous dynamical systems and for nonautonomous evolution equations
A modified strong squeezing property and the existence of inertial manifolds of semiflows
Cone invariance and squeezing properties for inertial manifolds for nonautonomous evolution equations
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.
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