Israel Journal of Mathematics

, Volume 51, Issue 3, pp 177–207 | Cite as

Feedback boundary control problems for linear semigroups

  • W. Desch
  • I. Lasiecka
  • W. Schappacher


We investigate the abstract Cauchy problem\(\frac{d}{{dt}}x(t) = A(I + B)x(t)\) and apply the obtained generation results to feedback boundary control problems.


Banach Space Linear Operator Strong Solution Hyperbolic Equation Boundary Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    J. Ball,Strongly continuous semigroups, weak solutions and the variation of constants formula, Proc. Am. Math. Soc.63 (1977), 370–373.zbMATHCrossRefGoogle Scholar
  2. 2.
    V. Barbu,Nonlinear Semigroups and Differential Equations in Banach Spaces, North-Holland, 1976.Google Scholar
  3. 3.
    H. Brezis,Operateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert, North-Holland, 1973.Google Scholar
  4. 4.
    S. Chang,Riccati equations for nonsymmetric and nondissipative hyperbolic systems, Ph.D. Thesis, Univ. of Florida, 1984.Google Scholar
  5. 5.
    J. Chazarain and J. Piriou,Introduction a la theorie des equations aux derivees partielles lineaires, Gauthier-Villars, 1981.Google Scholar
  6. 6.
    W. Desch and W. Schappacher,On relatively bounded perturbations of linear C 0 -semigroups, Ann. Sci. Norm. Super. Pisa11 (1984), 327–341.zbMATHMathSciNetGoogle Scholar
  7. 7.
    N. Dunford and J. Schwartz,Linear Operators I, Interscience, 1957.Google Scholar
  8. 8.
    K. O. Friedrichs and P. Lax,Boundary value problems for first order operators, Comm. Pure Appl. Math.18 (1965), 355–388.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    T. Kato,Perturbation Theory for Linear Operators, Springer, 1976.Google Scholar
  10. 10.
    H. O. Kreiss,Initial boundary value problems for hyperbolic equations, Comm. Pure Appl. Math.13 (1970), 277–298.CrossRefMathSciNetGoogle Scholar
  11. 11.
    I. Lasiecka and R. Triggiani,A cosine operator approach to modelling L 2(0,T, L 2(Γ))-boundary input hyperbolic equations, Appl. Math. Optim.7 (1981), 35–93.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    I. Lasiecka and R. Triggiani,Regularity of hyperbolic equations with L 2(0,T;L 2(Γ))Dirichlet boundary terms, Appl. Math. Optim.10 (1983), 275–286.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    I. Lasiecka and R. Triggiani,An L 2 theory for the quadratic optimal cost problem of hyperbolic equations, inControl Theory for Distributed Parameter Systems and Applications (F. Kappel, K. Kunisch and W. Schappacher, eds.), Springer Lecture Notes in Control and Information Sciences54 (1983), 138–152.Google Scholar
  14. 14.
    P. D. Lax and R. S. Phillips,Local boundary conditions for dissipative symmetric linear differential operators, Comm. Pure Appl. Math.13 (1960), 427–455.zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    A. Majda and S. Osher,Initial boundary value problems for hyperbolic equations with uniformly characteristic boundary, Comm. Pure Appl. Math.28 (1975), 607–676.zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    A. Pazy,Linear Semigroups and Applications, Springer, 1983.Google Scholar
  17. 17.
    J. Rauch,L 2 is a continuable initial condition for Kreiss’ Problems, Comm. Pure Appl. Math.25 (1972), 265–285.zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    R. Triggiani and I. Lasiecka,Boundary feedback stabilization problems for hyperbolic equations, inControl Theory for Distributed Parameter Systems and Applications (F. Kappel, K. Kunisch and W. Schappacher, eds.), Springer Lecture Notes in Control and Information Sciences54 (1983), 238–245.Google Scholar
  19. 19.
    R. Vinter and T. Johnson,Optimal control of nonsymmetric hyperbolic systems in n-variables in half spaces, SIAM J. Control15 (1977), 129–143.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© The Weizmann Science Press of Israel 1985

Authors and Affiliations

  • W. Desch
    • 1
  • I. Lasiecka
    • 2
  • W. Schappacher
    • 1
  1. 1.Institut für MathematikUniversität GrazGrazAustria
  2. 2.Department of MathematicsUniversity of FloridaGainesvilleUSA

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