Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors

More About This Textbook

Overview
Editorial Reviews
Product Details
Related Subjects
Table of Contents

Overview

"This book develops the theory of global attractors for a class of parabolic PDEs that includes reaction-diffusion equations and the Navier-Stokes equations, two examples that are treated in detail. A lengthy chapter on Sobolev spaces provides the framework that allows a rigorous treatment of existence and uniqueness of solutions for both linear time-independent problems (Poisson's equation) and the nonlinear evolution equations that generate the infinite-dimensional dynamical systems of the title. Attention then turns to the global attractor, a finite-dimensional subset of the infinite-dimensional phase space that determines the asymptotic dynamics. In particular, the concluding chapters investigate in what sense the dynamics restricted to the attractor are themselves "finite-dimensional."" "The book is intended as a didactic text for first-year graduate students and assumes only a basic knowledge of elementary functional analysis."--BOOK JACKET.

Editorial Reviews

From the Publisher

"The book is written clearly and concisely. It is well structured, and the material is presented in a rigorous, coherent fashion...[it] constitutes an excellent resource for researchers and advanced graduate students in applied mathematics, dynamical systems, nonlinear dynamics, and computational mechanics. Its acquisition by libraries is strongly recommended." Applied Mechanics Reviews

Product Details

ISBN-13: 9780521632041
Publisher: Cambridge University Press
Publication date: 5/28/2009
Series: Texts in Applied Mathematics Series , #28
Pages: 480
Product dimensions: 5.98 (w) x 8.98 (h) x 1.18 (d)

	Preface
	Introduction	1
Pt. I	Functional Analysis	9
1	Banach and Hilbert Spaces	11
2	Ordinary Differential Equations	42
3	Linear Operators	62
4	Dual Spaces	89
5	Sobolev Spaces	109
Pt. II	Existence and Uniqueness Theory	157
6	The Laplacian	159
7	Weak Solutions of Linear Parabolic Equations	188
8	Nonlinear Reaction-Diffusion Equations	213
9	The Navier-Stokes Equations: Existence and Uniqueness	234
Pt. III	Finite-Dimensional Global Attractors	259
10	The Global Attractor: Existence and General Properties	261
11	The Global Attractor for Reaction-Diffusion Equations	285
12	The Global Attractor for the Navier-Stokes Equations	309
13	Finite-Dimensional Attractors: Theory and Examples	325
Pt. IV	Finite-Dimensional Dynamics	357
14	The Squeezing Property: Determining Modes	359
15	The Strong Squeezing Property: Inertial Manifolds	385
16	A Direct Approach	406
17	The Kuramoto-Sivashinsky Equation	426
App. A	Sobolev Spaces of Periodic Functions	435
App. B	Bounding the Fractal Dimension Using the Decay of Volume Elements	439
	References	445
	Index	453

Customer Reviews

Be the first to write a review

( 0 )

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Poor

Below Average

Good

Very Good

Exceptional

Review Guidelines

Tell the world what you think of this product.

Add Recommendations

Your Name: Create a Pen Name or Leave Anonymously

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

- HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
- Time-sensitive information such as tour dates, signings, lectures, etc.
- Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
- Comments focusing on the author or that may ruin the ending for others
- Phone numbers, addresses, URLs
- Pricing and availability information or alternative ordering information
- Advertisements or commercial solicitation

Reminder:

- By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
- Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
- See Terms of Use for other conditions and disclaimers.

If you find inappropriate content, please report it to Barnes & Noble