Skip to main content
SpringerLink
Log in

Optimal obstacle control problem

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

In the paper we discuss some properties of the state operators of the optimal obstacle control problem for elliptic variational inequality. Existence, uniqueness and regularity of the optimal control problem are established. In addition, the approximation of the optimal obstacle problem is also studied.

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. Adams D R, Lenhart S. An obstacle control problem with a source term[J]. Appl Math Optim, 2003, 47(1):79–95.

    Article  MathSciNet  Google Scholar 

  2. Adams D R, Lenhart S. Optimal control of the obstacle for a parabolic variational inequality[J]. J Math Anal Appl, 2002, 268:602–614.

    Article  MATH  MathSciNet  Google Scholar 

  3. Adams D R, Lenhart S, Yong J. Optimal control of the obstacle for an elliptic variational inequality[J]. Appl Math Optim, 1998, 38:121–140.

    Article  MATH  MathSciNet  Google Scholar 

  4. Barbu V. Analysis and control of nonlinear infinite dimensional systems[M]. Math Sci Engrg 190, San Diego: Academic Press, 1993.

    Google Scholar 

  5. Chen Q. Indirect obstacle control problem for semilinear elliptic variational inequalities[J]. SIAM J Control Optim, 1999, 38:138–158.

    Article  MATH  MathSciNet  Google Scholar 

  6. Lou Hongwei. An optimal control problem governed by quasi-linear variational inequalities[J]. SIAM J Control Optim, 2003, 41(4):1229–1253.

    Article  Google Scholar 

  7. Chen Q. Optimal control for semilinear evolutionary variational bilateral problems[J]. J Math Anal Appl, 2003, 277(1):303–323.

    Article  MATH  MathSciNet  Google Scholar 

  8. Duvaunt G, Lions J L. Les inequations en mecanique et en physique[M]. Paris: Dunod, 1972.

    Google Scholar 

  9. Bergounioux M, Kunisch K. Augmented Lagrangian techniques for elliptic state constrained optimal control problems[J]. SIAM J Control Optim, 1997, 35:1524–1543.

    Article  MATH  MathSciNet  Google Scholar 

  10. Bergounioux M. Optimal control of semilinear elliptic obstacle problems[J]. J Nonlinear Convex Anal, 2002, 3(1):25–39.

    MATH  MathSciNet  Google Scholar 

  11. Chipot M. Variational inequalities and flow in porous media[M]. New York: Springer-Verlag, 1984.

    Google Scholar 

  12. Bergounioux M, Lenhart S. Optimal control of bilateral obstacle problems[J]. SIAM J Control Optim, 2004, 43(1):240–255.

    Article  MATH  MathSciNet  Google Scholar 

  13. Bucur D, Buttazzo G, Trabeschi P. An existence result for optimal obstacles[J]. J Funct Anal, 1999, 162(1):96–119.

    Article  MATH  MathSciNet  Google Scholar 

  14. Buttazzo G, Wagner A. On the optimal shape of a rigid body supported by an elastic membrane[J]. Nonlinear Anal, 2000, 39(1):47–63.

    Article  MathSciNet  Google Scholar 

  15. Zhang Gongqing, Lin Yuanqu. The functional analysis teaching materials[M]. Beijing: Beijing University Publication, 2003, 85 (in Chinese).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Xiangtan University, Xiangtan, 411105, Hunan Province, P. R. China

    Li Zhu  (朱砾)

  2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, P. R. China

    Xiu-hua Li  (李秀华) & Xing-ming Guo  (郭兴明)

Authors
  1. Li Zhu  (朱砾)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiu-hua Li  (李秀华)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xing-ming Guo  (郭兴明)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xing-ming Guo  (郭兴明).

Additional information

Contributed by GUO Xing-ming

Project supported by the National Natural Science Foundation of China (No. 10472061) and the Ph. D. Programs Foundation of Ministry of Education of China (No. 20060280015)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhu, L., Li, Xh. & Guo, Xm. Optimal obstacle control problem. Appl. Math. Mech.-Engl. Ed. 29, 559–569 (2008). https://doi.org/10.1007/s10483-008-0501-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-008-0501-5

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation