Skip to content
Register Sign in Wishlist
Infinite-Dimensional Dynamical Systems

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

£51.99

Part of Cambridge Texts in Applied Mathematics

  • Date Published: June 2001
  • availability: Available
  • format: Paperback
  • isbn: 9780521635646

£ 51.99
Paperback

Add to cart Add to wishlist

Other available formats:
Hardback


Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • This book develops the theory of global attractors for a class of parabolic PDEs which 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 which generate the infinite-dimensional dynamical systems of the title. Attention then switches to the global attractor, a finite-dimensional subset of the infinite-dimensional phase space which 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 graduates, and assumes only a basic knowledge of Banach and Hilbert spaces, and a working understanding of the Lebesgue integral.

    • Develops theory of PDEs as dynamical systems, theory of global attractors, and some consequences of that theory
    • Only a low level of previous knowledge of functional analysis is assumed, so accessible to the widest possible mathematical audience
    • Numerous exercises, with full solutions available on the web
    Read more

    Reviews & endorsements

    '… will certainly benefit young researchers entering the described field.' Jan Cholewa, Zentralblatt MATH

    'This impressive book offers an excellent, self-contained introduction to many important aspects of infinite-dimensional systems … At the outset, the author states that his aim was to produce a didactic text suitable or first-year graduate students. Unquestionably he has achieved his goal. This book should prove invaluable to mathematicians wishing to gain some knowledge of the dynamical-systems approach to dissipative partial differential equations that has been developed during the past 20 years, and should be essential reading for any graduate student starting out on a PhD in this area.' W. Lamb, Proceedings of the Edinburgh Mathematical Society

    'The book is written clearly and concisely. It is well structured, and the material is presented in a rigorous, coherent fashion. A number of example problems are treated, and each chapter is followed by a series of problems whose solutions are available on the internet. … 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

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: June 2001
    • format: Paperback
    • isbn: 9780521635646
    • length: 480 pages
    • dimensions: 229 x 152 x 27 mm
    • weight: 0.7kg
    • contains: 14 b/w illus.
    • availability: Available
  • Table of Contents

    Part I. Functional Analysis:
    1. Banach and Hilbert spaces
    2. Ordinary differential equations
    3. Linear operators
    4. Dual spaces
    5. Sobolev spaces
    Part II. Existence and Uniqueness Theory:
    6. The Laplacian
    7. Weak solutions of linear parabolic equations
    8. Nonlinear reaction-diffusion equations
    9. The Navier-Stokes equations existence and uniqueness
    Part II. Finite-Dimensional Global Attractors:
    10. The global attractor existence and general properties
    11. The global attractor for reaction-diffusion equations
    12. The global attractor for the Navier-Stokes equations
    13. Finite-dimensional attractors: theory and examples
    Part III. Finite-Dimensional Dynamics:
    14. Finite-dimensional dynamics I, the squeezing property: determining modes
    15. Finite-dimensional dynamics II, The stong squeezing property: inertial manifolds
    16. Finite-dimensional dynamics III, a direct approach
    17. The Kuramoto-Sivashinsky equation
    Appendix A. Sobolev spaces of periodic functions
    Appendix B. Bounding the fractal dimension using the decay of volume elements.

  • Resources for

    Infinite-Dimensional Dynamical Systems

    James C. Robinson

    General Resources

    Find resources associated with this title

    Type Name Unlocked * Format Size

    Showing of

    Back to top

    This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to lecturers whose faculty status has been verified. To gain access to locked resources, lecturers should sign in to or register for a Cambridge user account.

    Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other lecturers may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.

    Supplementary resources are subject to copyright. Lecturers are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.

    If you are having problems accessing these resources please contact lecturers@cambridge.org.

  • Author

    James C. Robinson, University of Warwick

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×