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Field name	Details
Dewey Class	514.34
Title	Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations ([EBook]) / by P. Constantin, C. Foias, B. Nicolaenko, R. Teman.
Author	Constantin, Peter. , 1951-
Added Personal Name	Foiaş, Ciprian
	Nicolaenko, B.
	Teman, R.
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer , 1989.
Physical Details	X, 123 pages : online resource.
Series	Applied mathematical sciences 0066-5452 ; ; 70
ISBN	9781461235064
Summary Note	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.:
Contents note	Preface -- Acknowledgments -- 1 Presentation of the Approach and of the Main Results -- 2 The Transport of Finite-Dimensional Contact Elements -- 3 Spectral Blocking Property -- 4 Strong Squeezing Property -- 5 Cone Invariance Properties -- 6 Consequences Regarding the Global Attractor -- 7 Local Exponential Decay Toward Blocked Integral Surfaces -- 8 Exponential Decay of Volume Elements and the Dimension of the Global Attractor -- 9 Choice of the Initial Manifold -- 10 Construction of the Inertial Manifold -- 11 Lower Bound for the Exponential Rate of Convergence to the Attractor -- 12 Asymptotic Completeness: Preparation -- 13 Asymptotic Completeness: Proof of Theorem 12.1 -- 14 Stability with Respect to Perturbations -- 15 Application: The Kuramoto—Sivashinsky Equation -- 16 Application: A Nonlocal Burgers Equation -- 17 Application: The Cahn—Hilliard Equation -- 18 Application: A Parabolic Equation in Two Space Variables -- 19 Application: The Chaffee—Infante Reaction—Diffusion Equation -- References.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4612-3506-4
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Complex manifolds . Manifolds and Cell Complexes (incl. Diff.Topology) . Manifolds (Mathematics) . Mathematical analysis . Mathematics . Authors: author . Constantin, Peter. 1951- . Constantin, Peter, 1951- . Foiaş, Ciprian . Foias. Ciprian . Nicolaenko, B. . Teman, R. . Corporate Authors: SpringerLink (Online service) . Series: Applied mathematical sciences . Classification: 514.34 .

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Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations

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