Published March 15, 1998
| public
Journal Article
Persistence of Invariant Sets for Dissipative Evolution Equations
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.
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.Additional details
- Eprint ID
- 78058
- DOI
- 10.1006/jmaa.1997.5847
- Resolver ID
- CaltechAUTHORS:20170609-123316540
- Los Alamos National Laboratory
- DMS-9308774
- NSF
- University of California
- Created
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2017-06-09Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
- Other Numbering System Name
- Andrew Stuart
- Other Numbering System Identifier
- J40