Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors (Cambridge Texts in Applied Mathematics) Book + PRICE WATCH * Amazon pricing is not included in price watch

Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors (Cambridge Texts in Applied Mathematics) Book

This book treats the theory of global attractors, a recent development in the theory of partial differential equations, in a way that also includes much of the traditional elements of the subject. As such it gives a quick but directed introduction to some fundamental concepts, and by the end proceeds to current research problems. Since the subject is relatively new, this is the first book to attempt to treat these various topics in a unified and didactic way. It is intended to be suitable for first year graduate students.Read More

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  • Product Description

    This book develops the theory of global attractors for a class of parabolic PDEs that 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 systemss 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.

  • 0521635640
  • 9780521635646
  • James C. Robinson
  • 16 April 2001
  • Cambridge University Press
  • Paperback (Book)
  • 480
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