Infinite-Dimensional Dynamical Systems

Official CUP webpage (including solutions).

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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. There are many exercises, and a full set of solutions is available to download from the web.

To download the PDF file containing the solutions to all the exercises click here

Click here for lectures notes from a course based on the book.

A list of errata can be found here. I would welcome an email if you find any others.

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