Infinite-Dimensional Dynamical Systems (inbunden)
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Format
Häftad (Trade paperback)
Språk
Engelska
Serie
Cambridge Texts in Applied Mathematics (del 28)
Antal sidor
480
Utgivningsdatum
2001-04-16
Förlag
Cambridge University Press
Dimensioner
230 x 153 x 26 mm
Vikt
640 g
ISBN
9780521635646

Infinite-Dimensional Dynamical Systems

An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors

av James C Robinson, James C Robinson
Häftad,  Engelska, 2001-04-16
824
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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.
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