Applied Mathematics and Mechanics

, Volume 24, Issue 7, pp 756–762 | Cite as

Optimal control of parabolic variational inequalities with state constraint

  • Guo Xing-ming
  • Zhou Shi-xing
Article

Abstract

The optimal control problem of parabolic variational inequalities with the state constraint and nonlinear, discontinuous nonmonotone multivalued mapping term and its approximating problem are studied, which generalizes some obtained results.

Key words

state constraint variational inequality discontinuous and nonmonotone nonlinear multivalued mapping optimal control 

Chinese Library Classification

O175.26 O178 

2000 MR Subject Classification

49J24 49J20 49J40 

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References

  1. [1]
    Barbu V.Optimal Control of Variational Inequalities[M]. London: Pitman, 1983.Google Scholar
  2. [2]
    Tiba D. Optimality conditions for distributed control problems with nonlinear state equation[J].SIAM J Control Optim, 1985,23(1):85–110.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Barbu V.Analysis and Control of Nonlinear Infinite Dimensional Systems[M]. Boston: Academic Press, Inc, 1993.Google Scholar
  4. [4]
    WANG Geng-sheng. Optimal control of parabolic variational inequality involving state constraint [J].Nonlinear Anal, 2000,42:789–801.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Mignot F, Puel J P. Optimal control in some variational inequalities[J].SIAM Control and Optim, 1984,22:466–476.MATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    GUO Xing-ming. On existence and uniqueness of solution of hyperbolic differential inclusion with discontinuous nonlinearity[J].J Math Anal Appl, 2000,241:198–213.MathSciNetCrossRefGoogle Scholar
  7. [7]
    Haslinger J, Panagiotopoulos P D. Optimal control of systems governed by hemivariational inequalities existence and approximation results[J].Nonlinear Anal, 1995,24(1):105–119.MATHMathSciNetCrossRefGoogle Scholar
  8. [8]
    Clarke F H.Optimization and Nonsmooth Analysis[M]. New York: Wiley, 1983.Google Scholar
  9. [9]
    Eberhard Zeidler.Nonlinear Functional Analysis and Its Applications-II/A:Linear Monotone Operators[M]. New York: Springer-Verlag, 1990.Google Scholar
  10. [10]
    Eberhard Zeidler.Nonlinear Functional Analysis and Its Applications-II/B:Nonlinear Monotone Operators[M]. New York: Springer-Verlag, 1990.Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2003

Authors and Affiliations

  • Guo Xing-ming
    • 1
  • Zhou Shi-xing
    • 1
  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghai University, Shanghai 200072P.R.China

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