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 .