Robinson, James C. The asymptotic completeness of inertial manifolds. (English) Zbl 0898.35016 Nonlinearity 9, No. 5, 1325-1340 (1996). Summary: An investigation of the asymptotic completeness property for inertial manifolds leads to the concept of ‘flow-normal hyperbolicity’, which is more natural in this case then the traditional form of normal hyperbolicity derived from the linearized flow near the manifold. An example shows that without flow-normal hyperbolicity asymptotic completeness cannot be guaranteed. The analysis also yields a new result on the asymptotic equivalence of ordinary differential equations. Cited in 14 Documents MSC: 35B40 Asymptotic behavior of solutions to PDEs 35G10 Initial value problems for linear higher-order PDEs 35K25 Higher-order parabolic equations 37D99 Dynamical systems with hyperbolic behavior Keywords:flow-normal hyperbolicity PDF BibTeX XML Cite \textit{J. C. Robinson}, Nonlinearity 9, No. 5, 1325--1340 (1996; Zbl 0898.35016) Full Text: DOI Link OpenURL