Infinite-Dimensional Dynamical Systems
Official CUP
webpage (including solutions).
Order from
www.amazon.co.uk
order from www.amazon.com (this webpage includes the table of contents
and full index)
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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