INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS by James C. Robinson ( 9780521635646 )

Item Details

Title:

INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS
AN INTRODUCTION TO DISSIPATIVE PARABOLIC PDES AND THE THEORY OF GLOBAL ATTRACTORS

By:

James C. Robinson

Format:

Paperback

List price:

£62.99

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£55.12

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£7.87

ISBN 10:

0521635640

ISBN 13:

9780521635646

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Publisher:

CAMBRIDGE UNIVERSITY PRESS

Pub. date:

16 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:

Imprint:

Cambridge University Press

Returns:

Returnable

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AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS

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ATTRACTORS FOR INFINITE-DIMENSIONAL NON-AUTONOMOUS DYNAMICAL SYSTEMS (HB)

ATTRACTORS FOR INFINITE-DIMENSIONAL NON-AUTONOMOUS DYNAMICAL SYSTEMS (PB)