Some remarks on the smoothness of inertial manifolds. (English) Zbl 0723.58033

Nonlinear evolutionary partial differential equations give rise to infinite dimensional dynamical systems. It is believed that dissipative effects may lead to the fact that in the long run only a finite number of degrees of freedom is relevant. This may be captured by the notion of the inertial manifold, producing a splitting of the Banach space with a subspace which is finite dimensional, invariant and exponentially attracting the solutions.
In the paper conditions for the existence of such inertial manifolds are given and regularity properties are shown.
Reviewer: C.H.Cap (Zürich)


37C70 Attractors and repellers of smooth dynamical systems and their topological structure
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
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