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.

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"The book is written clearly and concisely. It is well structured, and the material is presented in a rigorous, coherent fashion...[it] 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

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Product details

• Date Published: April 2001
• format: Paperback
• isbn: 9780521635646
• length: 480 pages

• dimensions: 229 x 152 x 27 mm
• weight: 0.7kg
• contains: 14 b/w illus.
• availability: Available