TY  - GEN
AU  - Robinson, James C.
TI  - Infinite-dimensional dynamical systems: an introduction to dissipative parabolic PDEs and the theory of global attractors
SN  - 9780521635646
U1  - 514.74 ROB 
PY  - 2001///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Dissipative Parabolic PDEs
KW  - Navier-Stokes Equations
KW  - Banach and Hilbert Spaces
KW  - Kuramoto-Sivashinsky Equation
KW  - Laplacian
KW  - Sobolev Spaces
N1  - Includes References and Index
N2  - 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.

Develops theory of PDEs as dynamical systems, theory of global attractors, and some consequences of that theory
Only a low level of previous knowledge of functional analysis is assumed, so accessible to the widest possible mathematical audience
Numerous exercises, with full solutions available on the web

https://www.cambridge.org/in/universitypress/subjects/mathematics/differential-and-integral-equations-dynamical-systems-and-co/infinite-dimensional-dynamical-systems-introduction-dissipative-parabolic-pdes-and-theory-global-attractors?format=PB
ER  -