SpringerLink
Log in

Stability of Exact Internal Synchronization by Groups

  • Chapter
  • First Online:
Synchronization for Wave Equations with Locally Distributed Controls

Part of the book series: Series in Contemporary Mathematics ((SCMA,volume 5))

  • 37 Accesses

Abstract

In this chapter, we will deepen the consideration in the previous chapter and show that the state variable can be divided into three groups: the first \((N-p)\) components will be exactly driven to any given target; the second \((p-q)\) components can be approximately driven to any given target; and the last q components are independent of applied controls.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
EUR 29.95
Price includes VAT (Thailand)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 96.29
Price includes VAT (Thailand)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
EUR 119.99
Price excludes VAT (Thailand)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Li, T.-T., Rao, B.-P.: Stability of exactly synchronizable state by groups for a coupled system of wave equations with respect to applied controls. Mathematical Control and Related Fields (2024). https://doi.org/10.3934/mcrf.2024008

  2. Lions, J.-L.: Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires. Dunod, Gauthier-Villars, Paris (1969)

    Google Scholar 

  3. Simon, J.: Compact sets in the space \(L^p(0, T; B)\). Ann. Mat. Pura Appl. 146, 65–97 (1986)

    Article  Google Scholar 

  4. Brezis, H.: Functional Analysis. Sobolev Spaces and Partial Differential Equations, Springer, New York (2011)

    Google Scholar 

  5. Li, T.-T., Rao, B.-P.: Boundary Synchronization for Hyperbolic Systems. Progress in Non Linear Differential Equations, Subseries in Control, vol. 94. Birkhäuser (2019)

    Google Scholar 

  6. Ciarlet, Ph.G.: Linear and Nonlinear Functional Analysis with Applications. Society for Industrial and Applied Mathematics, Philadelphia, PA (2013)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, Shanghai, China

    Tatsien Li

  2. Institut de Recherche Mathématique Avancée, University of Strasbourg, Strasbourg, France

    Bopeng Rao

Authors
  1. Tatsien Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bopeng Rao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tatsien Li .

Rights and permissions

Reprints and permissions

Copyright information

© 2024 Shanghai Scientific and Technical Publishers

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Li, T., Rao, B. (2024). Stability of Exact Internal Synchronization by Groups. In: Synchronization for Wave Equations with Locally Distributed Controls. Series in Contemporary Mathematics, vol 5. Springer, Singapore. https://doi.org/10.1007/978-981-97-0992-2_11

Download citation

Publish with us

Policies and ethics

Search

Navigation