Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic Pdes and the Theory of Global Attractors (Hardcover)

Descripción

Hardcover. 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

N° de ref. del artículo 9780521632041

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Detalles bibliográficos

Título

Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic Pdes and the Theory of Global Attractors (Hardcover)

Editor

Cambridge University Press, Cambridge

Fecha de publicación

2001

Idioma

Inglés

ISBN 10

0521632048

ISBN 13

9780521632041

Encuadernación

Hardcover

Edición

1ª Edición

Estado

new

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