Persistence of Invariant Sets for Dissipative Evolution Equations

Donald Jones; Andrew M. Stuart; Edriss S. Titi

doi:10.1006/jmaa.1997.5847

Persistence of Invariant Sets for Dissipative Evolution Equations

Donald Jones, Andrew M. Stuart, Edriss S. Titi

Mathematical and Statistical Sciences, School of (SoMSS)

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

16 Scopus citations

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 aC¹inertial form, certain natural numerical approximations possess an inertial form close to that of the underlying PDE in theC¹norm.

Original language	English (US)
Pages (from-to)	479-502
Number of pages	24
Journal	Journal of Mathematical Analysis and Applications
Volume	219
Issue number	2
DOIs	https://doi.org/10.1006/jmaa.1997.5847
State	Published - Mar 15 1998

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1006/jmaa.1997.5847

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title = "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 aC1inertial form, certain natural numerical approximations possess an inertial form close to that of the underlying PDE in theC1norm.",

author = "Donald Jones and Stuart, {Andrew M.} and Titi, {Edriss S.}",

note = "Funding Information: 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 NSE Grant DMS-9308774 and by the Joint University of California and Los Alamos National Laboratory INCOR program.",

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N2 - 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 aC1inertial form, certain natural numerical approximations possess an inertial form close to that of the underlying PDE in theC1norm.

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Persistence of Invariant Sets for Dissipative Evolution Equations

Abstract

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