Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic Pdes and the Theory of Global Attractors
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Book Overview
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.
Format:Paperback
Language:English
ISBN:0521635640
ISBN13:9780521635646
Release Date:August 2010
Publisher:Cambridge University Press
Length:480 Pages
Weight:1.45 lbs.
Dimensions:1.0" x 6.1" x 8.9"
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