Inertial manifolds for nonlinear evolutionary equations. (English) Zbl 0643.58004

Foias, Ciprian; Sell, George R.; Temam, Roger

J. Differ. Equations 73, No. 2, 309-353 (1988).

The authors introduce the concept of an inertial manifold for nonlinear evolutionary equations, including ordinary and partial differential equations. These finite dimensional Lipschitz-manifolds turn out to be appropriate to study the long-time behaviour of solutions of the evolutionary equations. In particular they contain the global attractor, attract exponentially all solutions and they are stable with respect to certain perturbations.
In the infinite dimensional case they allow the reduction of the dynamics to a finite dimensional ordinary differential equation.

Reviewer: N.Jacob

MSC:

37C70	Attractors and repellers of smooth dynamical systems and their topological structure
37L25	Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems

Keywords:

exponential attraction; inertial manifold; nonlinear evolutionary equations; long-time behaviour of solutions; global attractor

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