@article{e0cc87c5c6914982adf1a506691385f7,
title = "C1 approximations of inertial manifolds for dissipative nonlinear equations",
abstract = "In this paper we study a class of nonlinear dissipative partial differential equations that have inertial manifolds. This means that the long-time behavior is equivalent to a certain finite system of ordinary differential equations. We investigate ways in which these finite systems can be approximated in the C1 sense. Geometrically this may be interpreted as constructing manifolds in phase space that are C1 close to the inertial manifold of the partial differential equation. Under such approximations the invariant hyperbolic sets of the global attractor persist.",
author = "Jones, {Don A.} and Titi, {Edriss S.}",
note = "Funding Information: Part of this work was completed while D.A.J. was a Post-Doctoral Fellow at the Center for Turbulence Research at Stanford University, and while E.S.T. enjoyed the hospitality of the CNLS and the IGPP at the Los Alamos National Laboratory. E.S.T. was supported in part by the National Science Foundation grant number DMS-9308774, the Joint University of California Los Alamos National Laboratory Institute for Cooperative Research (INCOR) program for climate modeling and by the UC-Irvine Research Faculty Fellowship. D.A.J. was partially supported by the Department of Energy {\textquoteleft}{\textquoteleft}Computer Hardware, Advanced Mathematics, Model Physics{\textquoteright}{\textquoteright} (CHAMMP) research program as part of the U. S. Global Change Research Program.",
year = "1996",
month = may,
day = "1",
doi = "10.1006/jdeq.1996.0061",
language = "English (US)",
volume = "127",
pages = "54--86",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press Inc.",
number = "1",
}