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

Robinson, James C.

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.

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