| Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic Pdes and the Theory of Global Attractors Contributor(s): Robinson, James C. (Author) |
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ISBN: 0521635640 ISBN-13: 9780521635646 Publisher: Cambridge University Press OUR PRICE: $78.84 Product Type: Paperback - Other Formats Published: April 2001 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Topology - General - Mathematics | Applied |
| Dewey: 514.74 |
| LCCN: 00041413 |
| Series: Cambridge Texts in Applied Mathematics |
| Physical Information: 1.01" H x 6.13" W x 8.91" (1.39 lbs) 480 pages |