Mathematical Surveys and Monographs
Volume: 126;
2006;
184 pp;
Hardcover
MSC: Primary 35; 37; 47;
Print ISBN: 978-0-8218-4070-2
Product Code: SURV/126
List Price: $65.00
AMS Member Price: $52.00
MAA Member Price: $58.50
Electronic ISBN: 978-1-4704-1353-8
Product Code: SURV/126.E
List Price: $65.00
AMS Member Price: $52.00
MAA Member Price: $58.50
Supplemental Materials
Gradient Inequalities: with Applications to Asymptotic Behavior and Stability of Gradient-like Systems
Share this pageSen-Zhong Huang
This book presents a survey of the relatively new
research field of gradient inequalities and their applications. The exposition
emphasizes the powerful applications of gradient inequalities in studying
asymptotic behavior and stability of gradient-like dynamical systems. It
explains in-depth how gradient inequalities are established and how they can be
used to prove convergence and stability of solutions to gradient-like systems.
This book will serve as an introduction for further studies of gradient
inequalities and their applications in other fields, such as geometry and
computer sciences.
This book is written for advanced graduate students, researchers and applied
mathematicians interested in dynamical systems and mathematical
modeling.
Readership
Graduate students and research mathematicians interested in dynamical systems and PDEs.
Table of Contents
Table of Contents
Gradient Inequalities: with Applications to Asymptotic Behavior and Stability of Gradient-like Systems
- Contents v6 free
- Preface vii8 free
- Chapter 1 Introduction and overview of the results 110 free
- Chapter 2 Gradient inequality 2130
- 1. Basic properties of gradient maps 2130
- 2. Gradient inequality 2231
- 3. Finite-dimensional gradient inequality 2534
- 4. Infinite-dimensional gradient inequality 3443
- 5. Variational gradient inequality 4554
- 6. Gradient inequality for monotone gradient maps 4857
- 7. Optimal gradient inequality in Hilbert spaces 4958
- 8. Remarks on gradient inequalities of type G[sub(k)] 5160
- Chapter 3 Abstract convergence results 5968
- Chapter 4 Applications to semilinear gradient-like systems in Hilbert spaces 101110
- Chapter 5 Applications to the stability problem 163172
- Bibliography 177186
- Index 183192 free