Infinite-Dimensional Dynamical Systems
Format: Paperback
ISBN13: 9780521635646
Paperback|9780521635646
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Overview
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.
| ISBN-13 | 9780521635646 |
|---|---|
| ISBN-10 | 0521635640 |
| Weight | 1.54 Pounds |
| Dimensions | 6.00 x 1.20 x 9.00 In |
| List Price | $74.99 |
| Edition | 1st Edition |
| Format | Paperback |
|---|---|
| Language | English |
| Pages | 480 pages |
| Publisher | Cambridge University Press |
| Published On | 2001-04-16 |
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