Skip to main content
SpringerLink
Log in

Boundary stabilization of wave equations with variable coefficients

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

The aim of this paper is to obtain the exponential energy decay of the solution of the wave equation with variable coefficients under suitable linear boundary feedback. Multiplier method and Riemannian geometry method are used.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chen, G., Energy decay estimates and exact boundary value controllability for the wave equation in a bounded domain, J. Math. Pures. & Appl., 1979, 58: 249.

    MATH  MathSciNet  Google Scholar 

  2. Komornik, V., Exact controllability and stabilization, Research in Applied Mathematics (Series Editors: Ciarlet, P. G., Lions, J.), New York: Masson/John Wiley copublication, 1994.

    Google Scholar 

  3. Komornik, V., Zuazua, E., A direct method for the boundary stabilization of the wave equation, J. Math. Pures. & Appl., 1990, 69: 33.

    MATH  MathSciNet  Google Scholar 

  4. Lagnese, J., Decay of solutions of wave equations in a bounded region with boundary dissipation, J. Differential Equations, 1983, 50: 163.

    Article  MATH  MathSciNet  Google Scholar 

  5. Lasiecka, I., Triggiani, R., Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions, Appl. Math. & Optim., 1992, 25: 189.

    Article  MATH  MathSciNet  Google Scholar 

  6. Wyler, A., Stability of wave equations with dissipative boundary conditions in a bounded domain, Differential and Integral Equations, 1994, 7: 345.

    MATH  MathSciNet  Google Scholar 

  7. Yao, P. F., On the observability inequality for exact controllability of wave equations with variable coefficients, SIAM J. Control & Optimization, 1999, 37, 5: 1568.

    Article  MATH  Google Scholar 

  8. Wu, H., Shen, C. L., Yu, Y. L., Introduction to Riemannian Geometry (in Chinese), Beijing: Peking University Press, 1989.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100080, Beijing, China

    Shaoji Feng & Dexing Feng

Authors
  1. Shaoji Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dexing Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shaoji Feng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Feng, S., Feng, D. Boundary stabilization of wave equations with variable coefficients. Sci. China Ser. A-Math. 44, 345–350 (2001). https://doi.org/10.1007/BF02878715

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02878715

Keywords

Search

Navigation