Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors: 28 (Cambridge Texts in Applied Mathematics, Series Number 28) - Hardcover

Robinson, James C.

Hardcover

ISBN 10: 0521632048 ISBN 13: 9780521632041

Publisher: Cambridge University Press, 2001

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.

About this title

Review

'... will certainly benefit young researchers entering the described field.' Jan Cholewa, Zentralblatt MATH

'This impressive book offers an excellent, self-contained introduction to many important aspects of infinite-dimensional systems ... At the outset, the author states that his aim was to produce a didactic text suitable or first-year graduate students. Unquestionably he has achieved his goal. This book should prove invaluable to mathematicians wishing to gain some knowledge of the dynamical-systems approach to dissipative partial differential equations that has been developed during the past 20 years, and should be essential reading for any graduate student starting out on a PhD in this area.' W. Lamb, Proceedings of the Edinburgh Mathematical Society

'The book is written clearly and concisely. It is well structured, and the material is presented in a rigorous, coherent fashion. A number of example problems are treated, and each chapter is followed by a series of problems whose solutions are available on the internet. ... constitutes an excellent resource for researchers and advanced graduate students in applied mathematics, dynamical systems, nonlinear dynamics, and computational mechanics. Its acquisition by libraries is strongly recommended.' Applied Mechanics Reviews

Book Description

This book treats the theory of global attractors, a recent development in the theory of partial differential equations, in a way that also includes many traditional elements of the subject. It gives a quick but directed introduction to some fundamental concepts, and by the end proceeds to current research problems.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2001
• Language: English
• ISBN 10: 0521632048
• ISBN 13: 9780521632041
• Binding: Hardcover
• Number of pages: 480