04115nam a22005775i 4500 978-981-97-0992-2 DE-He213 20251030112238.0 cr nn 008mamaa 240528s2024 si | s |||| 0|eng d 9789819709922 978-981-97-0992-2 10.1007/978-981-97-0992-2 doi Q295 QA402.3-402.37 GPFC bicssc SCI064000 bisacsh GPFC thema Li, Tatsien. author. aut http://id.loc.gov/vocabulary/relators/aut 77644 Synchronization for Wave Equations with Locally Distributed Controls [electronic resource] / by Tatsien Li, Bopeng Rao. 1st ed. 2024. Singapore : Springer Nature Singapore : Imprint: Springer, 2024. IX, 199 p. 3 illus., 2 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Series in Contemporary Mathematics, 2364-0103 ; 5 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. 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. System theory. 66519 Control theory. 68675 Differential equations. Functional analysis. Systems Theory, Control. 68676 Differential Equations. Functional Analysis. Rao, Bopeng. author. aut http://id.loc.gov/vocabulary/relators/aut 77645 SpringerLink (Online service) Springer Nature eBook Printed edition: 9789819709915 Printed edition: 9789819709939 Printed edition: 9789819709946 Series in Contemporary Mathematics, 2364-0103 ; 5 77646 https://doi.org/10.1007/978-981-97-0992-2 ZDB-2-SMA ZDB-2-SXMS 60222 60222