Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors

di James C. Robinson (Autore)

Cambridge University Press, 2001

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.

• Autore: James C. Robinson
• Editore: Cambridge University Press
• Collana: Cambridge Texts in Applied Mathematics
• Anno: 2001
• Rilegatura: Paperback / softback
• Pagine: 480 p.
• Dimensioni: 229 x 152 mm
• Peso: 700 gr.
• EAN: 9780521635646

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