Infinite-Dimensional Dynamical Systems

An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors

By:

James C Robinson

Format:

Hardback

Series:

Cambridge Texts in Applied Mathematics

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Description

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.

Release date NZ

April 23rd, 2001

Author

James C Robinson

Audience

Professional & Vocational

Illustrations

14 Line drawings, unspecified

Pages

480

Series

Cambridge Texts in Applied Mathematics

Dimensions

160x236x31

ISBN-13

9780521632041

Product ID

2011785

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