Inertial manifolds: The non-self-adjoint case

George R. Sell; Yuncheng You

doi:10.1016/0022-0396(92)90152-D

Inertial manifolds: The non-self-adjoint case

George R. Sell, Yuncheng You

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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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 language	English (US)
Pages (from-to)	203-255
Number of pages	53
Journal	Journal of Differential Equations
Volume	96
Issue number	2
DOIs	https://doi.org/10.1016/0022-0396(92)90152-D
State	Published - 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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10.1016/0022-0396(92)90152-D

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author = "Sell, {George R.} and Yuncheng You",

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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AU - You, Yuncheng

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N2 - 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.

AB - 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.

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Inertial manifolds: The non-self-adjoint case

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