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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.
Table of contents:
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 problems; 6. Examples of global attractors in parabolic problems; 7. Backward uniqueness and regularity of solutions; 8. Extensions; Appendix.
Dissipative equations have attracted substantial attention over many years. This book uses both finite and infinite dimensional techniques to investigate the asymptotic behaviour of dynamical systems corresponding to parabolic equations. 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.
This book investigates the asymptotic behaviour of dynamical systems corresponding to parabolic equations.
Table of contents:
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 problems; 6. Examples of global attractors in parabolic problems; 7. Backward uniqueness and regularity of solutions; 8. Extensions; Appendix.
Dissipative equations have attracted substantial attention over many years. This book uses both finite and infinite dimensional techniques to investigate the asymptotic behaviour of dynamical systems corresponding to parabolic equations. 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.
This book investigates the asymptotic behaviour of dynamical systems corresponding to parabolic equations.