Skip to main content
SpringerLink
Log in

Proof of two conjectures by G. Chen and D. L. Russell on structural damping for elastic systems

  • Optimization Theory
  • Conference paper
  • First Online:
Approximation and Optimization

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1354))

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Chen and D. L. Russell, A mathematical model for linear elastic systems with structural damping, Quarterly of Applied Mathematics, Jan. 1982, 433–454.

    Google Scholar 

  2. S. Chen and R. Triggiani, Proof of extension of two conjectures of G. Chen and D. L. Russell on structural damping for general elastic systems, to appear.

    Google Scholar 

  3. N. Dunford, A survey of the theory of spectral operators, Bulletin Amer. Math. Soc., 64, 5, (1958), 217–274.

    Article  MathSciNet  MATH  Google Scholar 

  4. N. Dunford and J. Schwartz, Linear Operators, I (1958), II (1963), III (1971), Interscience Pubs, John Wiley, New York.

    MATH  Google Scholar 

  5. H. O. Fattorini, The Cauchy Problem, Encyclopedia of Mathematics and its Applications Addison-Wesley, Benjamin/Cummings Inc., Reading, Massachusetts 01867, 1983.

    Google Scholar 

  6. T. Kato, Perturbation of Linear Operators, Springer-Verlag, New York, 1966.

    Book  MATH  Google Scholar 

  7. S. G. Krein, Linear Differential Equations in Banach Space, Translations American Mathematical Society Vol 29, American Mathematical Society, Providence, Rhode Island 02904, 1971.

    Google Scholar 

  8. J. L. Lions and E. Magenes, Nonhomogeneous Boundary Value Problems, Vol. I, Springer-Verlag, New York, 1972.

    Book  MATH  Google Scholar 

  9. I. Lasiecka and R. Triggiani, Finite rank, relatively bounded perturbations of Co-semigroups, Part II: Spectrum allocation and Riesz basis in parabolic and hyperbolic feedback systems, Annali Matematica Pura e Applicata IV, Vol. CXLIII (1986), 47–100.

    Article  MathSciNet  MATH  Google Scholar 

  10. I. Lasiecka and R. Triggiani, Feedback semigroups and cosine operators for boundary feedback parabolic and hyperbolic equations, J. Differ. Equats. 47(1983), 246–272.

    Article  MathSciNet  Google Scholar 

  11. A. Pazy, Semigroups of Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.

    Book  MATH  Google Scholar 

  12. M. Schechter, Principles of Functional Analysis, Academic Press, New York, 1971.

    MATH  Google Scholar 

  13. A. E. Taylor and D. C. Lay, Introduction to Functional Analysis, Second Edition, John Wiley & Sons, 1980.

    Google Scholar 

  14. R. Triggiani, Improving stability properties of hyperbolic damped equations by boundary feedback, Springer-Verlag Lecture Notes LNCIS (1985), 400–409.

    Google Scholar 

  15. D. Xia, Spectral Theory of Hyponormal Operators, Birkhauser Verlag, Basel-Boston-Stuttgart, 1983.

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, China

    Shuping Chen

  2. Department of Mathematics, University of Florida, 32611, Gainesville, Florida

    Roberto Triggiani

  3. Department of Applied Mathematics, Thornton Hall, University of Virginia, 22903, Charlottesville, Virginia

    Roberto Triggiani

Authors
  1. Shuping Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roberto Triggiani
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Juan Alfredo Gómez-Fernandez Francisco Guerra-Vázquez Guillermo López-Lagomasino Miguel A. Jiménez-Pozo

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Chen, S., Triggiani, R. (1988). Proof of two conjectures by G. Chen and D. L. Russell on structural damping for elastic systems. In: Gómez-Fernandez, J.A., Guerra-Vázquez, F., López-Lagomasino, G., Jiménez-Pozo, M.A. (eds) Approximation and Optimization. Lecture Notes in Mathematics, vol 1354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089601

Download citation

  • DOI: https://doi.org/10.1007/BFb0089601

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50443-6

  • Online ISBN: 978-3-540-46005-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation