Inertial manifolds: The non-self-adjoint case

George R. Sell, Yuncheng You

Research output: Contribution to journalArticlepeer-review

42 Scopus citations

Abstract

In contrast with the existing theories of inertial manifolds, which are based on the self-adjoint assumption of the principal differential operator, in this paper we show that for general dissipative evolutionary systems described by semilinear parabolic equations with principal differential operator being sectorial and having compact resolvent, there exists an inertial manifold provided that certain gap conditions hold. We also show that by using an elliptic regularization, this theory can be extended to a class of KdV equations, where the principal differential operator is not sectorial.

Original languageEnglish (US)
Pages (from-to)203-255
Number of pages53
JournalJournal of Differential Equations
Volume96
Issue number2
DOIs
StatePublished - Apr 1992

Bibliographical note

Funding Information:
*This work was supported in part with grants from the National Science Foundation, the Applied and Computational Mathematics Program/DARPA, and the Army Research Office.

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