Global Attractors in Abstract Parabolic Problems

This book investigates the asymptotic behaviour of dynamical systems corresponding to parabolic equations.

Jan W. Cholewa (Author), Tomasz Dlotko (Author)

9780521794244, Cambridge University Press

Paperback, published 31 August 2000

248 pages
22.8 x 15.3 x 1.7 cm, 0.36 kg

"The general tools that the book presents, oriented to obtaining the existence of global attractors, the compilation of results on semilinear equations, the large variety and number of concrete examples and the collection of references, make the book a good reference for introducing the reader in to the vast literature on dissipative systems." Mathematical Reviews

The study of dissipative equations is an area that has attracted substantial attention over many years. Much progress has been achieved using a combination of both finite dimensional and infinite dimensional techniques, and in this book the authors exploit these same ideas to investigate the asymptotic behaviour of dynamical systems corresponding to parabolic equations. In particular the theory of global attractors is presented in detail. Extensive auxiliary material and rich references make this self-contained book suitable as an introduction for graduate students, and experts from other areas, who wish to enter this field.

Preface
1. Preliminary concepts
2. The abstract Cauchy problem
3. Semigroups of global solutions
4. Construction of the global attractor
5. Application of abstract results to parabolic equations
6. Examples of global attractors in parabolic problems
7. Backward uniqueness and regularity of solutions
8. Extensions
9. Appendix
Bibliography
Index.

Subject Areas: Applied mathematics [PBW]