1997 | OriginalPaper | Buchkapitel
Non-Well-Posed Problems, Unstable Manifolds, Lyapunov Functions, and Lower Bounds on Dimensions
verfasst von : Roger Temam
Erschienen in: Infinite-Dimensional Dynamical Systems in Mechanics and Physics
Verlag: Springer New York
Enthalten in: Professional Book Archive
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
This corresponds to the case where the semigroup S(t) is not defined everywhere, or is not defined for all times t. In that case, a concept of functionalinvariant sets can be introduced by modifying slightly that given in Chapter I. Of course, we can no longer expect to prove the existence of absorbing sets and attractors, and the results of Chapter I do not apply anymore. However, the results of Chapter V concerning the dimensions of invariant sets have been proved at a level of generality which makes them applicable to such situations. Some examples are given without any attempt at generality.