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InfiniteDimensional Dynamical Systems An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors - Cambridge Texts in Applied Mathematics
Author: James C. Robinson

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...  more » 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.  « less

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ISBN-13: 9780521632041
ISBN-10: 0521632048
Publication Date: 4/23/2001
Pages: 480
Edition: 1
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Publisher: Cambridge University Press
Book Type: Hardcover
Other Versions: Paperback
Members Wishing: 0
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