Infinite-dimensional dynamical systems : an introduction to dissipative parabolic PDEs and the theory of global attractors
Infinite-dimensional dynamical systems : an introduction to dissipative parabolic PDEs and the theory of global attractors By James C Robinson
2001 | 473 Pages | ISBN: 0521632048 | DJVU | 3 MB
2001 | 473 Pages | ISBN: 0521632048 | DJVU | 3 MB
"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 that generate the infinite-dimensional dynamical systems of the title. Attention then turns to the global attractor, a finite-dimensional subset of the infinite-dimensional phase space that 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 graduate students and assumes only a basic knowledge of elementary functional analysis."--BOOK JACKET.