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Approximation of dissipative partial differential equations over long time intervals

Humphries, A. R. and Jones, D. A. and Stuart, A. M. (1994) Approximation of dissipative partial differential equations over long time intervals. In: Numerical Analysis 1993. Pitman Research Notes in Mathematics Series . No.303. Longman Scientific & Technical , pp. 180-207. ISBN 9780582225688. https://resolver.caltech.edu/CaltechAUTHORS:20170612-152618052

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Abstract

In this article the numerical analysis of dissipative semilinear evolution equations with sectorial linear part is reviewed. In particular the approximation theory for such equations over long time intervals is discussed. Emphasis is placed on studying the effect of approximation on certain invariant objects which play an important role in understanding long time dynamics. Specifically the existence of absorbing sets, the upper and lower semicontinuity of global attractors and the existence and convergence of attractive invariant manifolds, such as the inertial manifold and unstable manifolds of equilibrium points, is studied.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://www.crcpress.com/Numerical-Analysis-1993/Griffiths-Watson/p/book/9780582225688PublisherBook
Additional Information:© 1994 Longman Scientific & Technical. This research was supported by the NSF contract DMS-9201727 and ONR contract N00014-92-J-1876.
Funders:
Funding AgencyGrant Number
NSFDMS-9201727
Office of Naval Research (ONR)N00014-92-J-1876
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartC3
Series Name:Pitman Research Notes in Mathematics Series
Issue or Number:303
Record Number:CaltechAUTHORS:20170612-152618052
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170612-152618052
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78127
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:13 Jun 2017 16:22
Last Modified:03 Oct 2019 18:05

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