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Infinite-dimensional dynamical systems : an introduction to dissipative parabolic PDEs and the theory of global attractors
Autor: James C. Robinson
Rok: 2001
ISBN: 9780521635646
NKP-CNB: bod004-mub01000358712
OKCZID: 110060277
Citace (dle ČSN ISO 690):
ROBINSON, James C. Infinite-dimensional dynamical systems: an introduction to dissipative parabolic PDEs and the theory of global attractors. Cambridge: Cambridge University Press, c2001. xvii, 461 s. Cambridge texts in applied mathematics.
Anotace
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.