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

Author: Robinson, James C.

Brand: Cambridge University Press

Binding: paperback

Number Of Pages: 461

Release Date: 01-04-2001

Part Number: 14 b/w illus.

Details: 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.

EAN: 9780521635646

Package Dimensions: 8.8 x 6.1 x 1.1 inches

Languages: English