---

＜電子ブック＞
Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations / by P. Constantin, C. Foias, B. Nicolaenko, R. Temam
(Applied Mathematical Sciences. ISSN:2196968X ; 70)

版	1st ed. 1989.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	1989
本文言語	英語
大きさ	X, 123 p : online resource
冊子体	Integral manifolds and inertial manifolds for dissipative partial differential equations / P. Constantin ... [et al.] ; : us,: gw
著者標目	*Constantin, P author Foias, C author Nicolaenko, B author Temam, R author SpringerLink (Online service)
件　名	LCSH:Manifolds (Mathematics) LCSH:Mathematical analysis FREE:Manifolds and Cell Complexes FREE:Analysis
一般注記	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 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-1-4612-3506-4

 類似資料