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Opis

This book develops the theory of global attractors for a class of parabolic PDEs which 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 systems 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.

Szczegóły książki

Kategoria Książki po angielsku Mathematics & science Mathematics Calculus & mathematical analysis

• Pełny tytuł: Infinite-Dimensional Dynamical Systems
• Podtytuł: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors
• Autor: James C. (University of Warwick) Robinson
• Język: Angielski
• Oprawa: Miękka
• Liczba stron: 480
• EAN: 9780521635646
• ISBN: 0521635640
• ID: 02038424
• Wydawca: Cambridge University Press
• Waga: 718 g
• Wymiary: 155 × 231 × 35 mm
• Data wydania: 16. April 2001

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