Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations

P. Constantin, R. Temam, B. Nicolaenko, C. Foias

ISBN 10: 1461281318 / ISBN 13: 9781461281313

Published by Springer New York, 2011

About this Item

Zustand: Hervorragend | Sprache: Englisch | Produktart: Bücher | This work was initiated in the summer of 1985 while all of the authors were at the Center of Nonlinear Studies of the Los Alamos National Laboratory; it was then continued and polished while the authors were at Indiana Univer­ sity, at the University of Paris-Sud (Orsay), and again at Los Alamos in 1986 and 1987. Our aim was to present a direct geometric approach in the theory of inertial manifolds (global analogs of the unstable-center manifolds) for dissipative partial differential equations. This approach, based on Cauchy integral mani­ folds for which the solutions of the partial differential equations are the generating characteristic curves, has the advantage that it provides a sound basis for numerical Galerkin schemes obtained by approximating the inertial manifold. The work is self-contained and the prerequisites are at the level of a graduate student. The theoretical part of the work is developed in Chapters 2-14, while in Chapters 15-19 we apply the theory to several remarkable partial differ­ ential equations.

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Bibliographic Details

• Title: Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations
• Publisher: Springer New York
• Publication Date: 2011
• Language: English
• ISBN 10: 1461281318
• ISBN 13: 9781461281313
• Binding: Soft cover
• Condition: Hervorragend
• Seller catalogs:
  • Bücher

About this title

Synopsis

This work was initiated in the summer of 1985 while all of the authors were at the Center of Nonlinear Studies of the Los Alamos National Laboratory; it was then continued and polished while the authors were at Indiana Univer­ sity, at the University of Paris-Sud (Orsay), and again at Los Alamos in 1986 and 1987. Our aim was to present a direct geometric approach in the theory of inertial manifolds (global analogs of the unstable-center manifolds) for dissipative partial differential equations. This approach, based on Cauchy integral mani­ folds for which the solutions of the partial differential equations are the generating characteristic curves, has the advantage that it provides a sound basis for numerical Galerkin schemes obtained by approximating the inertial manifold. The work is self-contained and the prerequisites are at the level of a graduate student. The theoretical part of the work is developed in Chapters 2-14, while in Chapters 15-19 we apply the theory to several remarkable partial differ­ ential equations.