| Title:
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INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS
AN INTRODUCTION TO DISSIPATIVE PARABOLIC PDES AND THE THEORY OF GLOBAL ATTRACTORS |
| By: |
James C. Robinson, Mark J. Ablowitz, S. H. Davis |
| Format: |
Hardback |
| List price:
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£147.00 |
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£128.63 |
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£18.37 |
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| ISBN 10: |
0521632048 |
| ISBN 13: |
9780521632041 |
| Availability: |
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| Publisher: |
CAMBRIDGE UNIVERSITY PRESS |
| Pub. date: |
23 April, 2001 |
| Series: |
Cambridge Texts in Applied Mathematics 28 |
| Pages: |
480 |
| Description: |
This book treats the theory of global attractors, a recent development in the theory of partial differential equations. |
| Synopsis: |
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. |
| Illustrations: |
14 b/w illus. |
| Publication: |
UK |
| Imprint: |
Cambridge University Press |
| Returns: |
Returnable |