Jones, Don A. and Stuart, Andrew M. and Titi, Edriss S. (1998) Persistence of Invariant Sets for Dissipative Evolution Equations. Journal of Mathematical Analysis and Applictions, 219 (2). pp. 479-502. ISSN 0022-247X. doi:10.1006/jmaa.1997.5847. https://resolver.caltech.edu/CaltechAUTHORS:20170609-123316540
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Abstract
We show that results concerning the persistence of invariant sets of ordinary differential equations under perturbation may be applied directly to a certain class of partial differential equations. Our framework is particularly well-suited to encompass numerical approximations of these partial differential equations. Specifically, we show that for a class of PDEs with aC^1 inertial form, certain natural numerical approximations possess an inertial form close to that of the underlying PDE in theC^1 norm.
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| Additional Information: | © 1998 Academic Press. Received 9 December 1996. We thank Steve Shkoller and Tony Shardlow for their careful reading of the manuscript and for their helpful suggestions. D.A.J. and E.S.T. gratefully acknowledge the support of the Institute for Geophysics and Planetary Physics (IGPP) and the Center for Nonlinear Studies (CNLS) at Los Alamos National Laboratory. This work was supported in part by the NSF Grant DMS-9308774 and by the Joint University of California and Los Alamos National Laboratory INCOR program. | |||||||||
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| Issue or Number: | 2 | |||||||||
| DOI: | 10.1006/jmaa.1997.5847 | |||||||||
| Record Number: | CaltechAUTHORS:20170609-123316540 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170609-123316540 | |||||||||
| Official Citation: | Don A Jones, Andrew M Stuart, Edriss S Titi, Persistence of Invariant Sets for Dissipative Evolution Equations, Journal of Mathematical Analysis and Applications, Volume 219, Issue 2, 1998, Pages 479-502, ISSN 0022-247X, http://dx.doi.org/10.1006/jmaa.1997.5847. (http://www.sciencedirect.com/science/article/pii/S0022247X97958479) | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 78058 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 09 Jun 2017 21:26 | |||||||||
| Last Modified: | 15 Nov 2021 17:36 |
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