Synchronization for Wave Equations with Locally Distributed Controls

This book aims to establish a systematic theory on the synchronization for wave equations with locally distributed controls. It is structured in two parts. Part I is devoted to internal controls, while Part II treats the case of mixed internal and boundary controls. The authors present necessary mathematical formulations and techniques for analyzing and solving problems in this area. They also give numerous examples and applications to illustrate the concepts and demonstrate their practical relevance.

The book provides an overview of the field and offers an in-depth analysis of new results with elegant proofs. By reading this book, it can be found that due to the use of internal controls, more deep-going results on synchronization can be obtained, which makes the corresponding synchronization theory more precise and complete.

Graduate students and researchers in control and synchronization for partial differential equations, functional analysis find this book useful. It is also an excellent reference in the field. Thanks to the explicit criteria given in this book for various notions of controllability and synchronization, researchers and practitioners can effectively use the control strategies described in this book and make corresponding decisions regarding system design and operation.

Provides a systematic theory on the internal synchronization for system of wave equations Presents necessary mathematical formulations and techniques for analyzing and solving problems in this area Gives numerous examples and applications to illustrate the concepts and demonstrate their practical relevance

Autorentext
Tatien Li is a professor at Fudan University; he is also a member of the Chinese Academy of Sciences and a foreign member of the French Academy of Science while Bopeng Rao is a professor at Strasbourg University. Both authors are specialists of control theory.

Zusammenfassung

This book is an invaluable resource for graduate students and researchers working in control theory, synchronization, and the broader study of partial differential equations and functional analysis. ... This book provides a rigorous and accessible guide to the synchronization of wave equations. (Kaïs Ammari, zbMATH 1555.35002, 2025)

Inhalt

1. Introduction.- 2. Algebraic preliminaries.- 3. Approximate internal controllability.- 4. Indirect internal controls.- 5. Approximate internal synchronization.- 6. Approximate internal synchronization by groups.- 7. Exact internal controllability.- 8. Exact internal synchronization.- 9. Stability of exact internal synchronization.- 10. Exact internal synchronization by groups.- 11. Stability of exact internal synchronization by groups.- 12. Family of exact internal synchronizations.- 13. Approximate mixed controllability.- 14. Approximate mixed synchronization by groups.- 15. Exact mixed controllability.- 16. Exact mixed synchronization by groups.