A Modified Strong Squeezing Property and the Existence of Inertial Manifolds of Semiflows

Norbert Koksch

Address. TU Dresden, FR Mathematik, 01062 Dresden, Germany

E-mail: koksch@math.tu-dresden.de

Abstract. Sometimes so-called cone invariance and squeezing properties are used to show the existence of inertial manifolds for evolution equations. We propose and motivate a modification of these properties for semiflows. We show 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.

AMSclassification. 37L25, 37D10, 34C30, 35B42, 35K90

Keywords. Semiflow, inertial manifold, asymptotic phase, cone invariance property, squeezing property .