Infinite-Dimensional Dynamical Systems
An Introduction To Dissipative Parabolic Pdes And The Theory Of Global Attractors
- Editore:
Cambridge University Press
- EAN:
9780521632041
- ISBN:
0521632048
- Pagine:
- 480
- Formato:
- Hardback
- Lingua:
- Inglese
Descrizione Infinite-Dimensional Dynamical Systems
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.
