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The asymptotic completeness of inertial manifolds. (English) Zbl 0898.35016

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.

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
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