The study of dissipative equations has attracted substantial attention over many years. Much progress has been achieved using a combination of both finite dimensional and infinite dimensional techniques. In this book the authors exploit these same ideas to investigate the asymptotic behavior of dynamical systems corresponding to parabolic equations. In particular they present the theory of global attractors in detail. Extensive auxiliary material and rich references make this self-contained book a suitable introduction for graduate students.
Contents
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.
Review
"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
Printer friendly version