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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 which generate the infinite-dimensional dynamical systemss 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.
- Sales Rank: #3361780 in Books
- Published on: 2001-04-23
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x 1.18" w x 5.98" l, 1.92 pounds
- Binding: Hardcover
- 480 pages
Review
"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
About the Author
Previous books by this editor: Acta Numerica 1992 - 2003 (Vols 1 - 12); as author: First Course in the Numerical Analysis of Differential Equations (0521 553768), Approximation Theory and Optimization (0521 581907).
Most helpful customer reviews
1 of 1 people found the following review helpful.
It's great
By yzhou
I read it several times it is not easy but clear and good for you to learn the dynamic systems. Anyway weath to buy.
0 of 0 people found the following review helpful.
Five Stars
By jp
complete review of the subject
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