INFINITE DIMENSION DYNAMIC SYSTEMS

INFINITE DIMENSION DYNAMIC SYSTEMS

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.
Editora: CAMBRIDGE UNIVERSITY PRESS
ISBN: 0521635640
ISBN13: 9780521635646
Edição: 1ª Edição - 2001
Número de Páginas: 480
Acabamento: PAPERBACK
Formato: 15.40 x 22.40 cm.
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