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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.

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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
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Additional Information:© 1994 Longman Scientific & Technical. This research was supported by the NSF contract DMS-9201727 and ONR contract N00014-92-J-1876.
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-92-J-1876
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Andrew StuartC3
Series Name:Pitman Research Notes in Mathematics Series
Issue or Number:303
Record Number:CaltechAUTHORS:20170612-152618052
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78127
Deposited By: Ruth Sustaita
Deposited On:13 Jun 2017 16:22
Last Modified:03 Oct 2019 18:05

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