A modified strong squeezing property and the existence of inertial manifolds of semiflows. (English) Zbl 1072.37053

Sometimes so-called cone invariance and squeezing properties are used to show the existence of inertial manifolds for evolution equations. The author propose and motivate a modification of these properties for semiflows. It is shown that the cone invariance and modified squeezing properties together with a coercivity assumption are sufficient for a general, continuous semiflow to have an inertial manifold with exponential tracking property. An application to evolution equations is considered and some possible extensions are discussed as well.


37L25 Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems
37D10 Invariant manifold theory for dynamical systems
34C30 Manifolds of solutions of ODE (MSC2000)
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