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Book 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.

Book details

Book category Books in English Mathematics & science Mathematics Calculus & mathematical analysis

• Full title: Infinite-Dimensional Dynamical Systems
• Subtitle: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors
• Author: James C. (University of Warwick) Robinson
• Language: English
• Binding: Paperback
• Number of pages: 480
• EAN: 9780521635646
• ISBN: 0521635640
• ID: 02038424
• Publisher: Cambridge University Press
• Weight: 718 g
• Dimensions: 155 × 231 × 35 mm
• Date of publishing: 16. April 2001

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