Semigroup Forum

, Volume 38, Issue 1, pp 233–251

Integrated semigroups and their application to complete second order cauchy problems

  • Frank Neubrander
Research Article


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    W. Arendt,Vector valued Lrplace transforms and Cauchy problems, Israel J. Math.59 (1987), 327–352.MATHMathSciNetGoogle Scholar
  2. [2]
    W. Arendt, H. Kellermann,Integrated solutions of Volterra integro-differential equations and applications, Preprint 1987.Google Scholar
  3. [3]
    P. Aviles, J. Sandefur,Nonlinear second order equations with applications to partial differential equations, J. Diff. Eqns.58 (1985), 404–427.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    R. Beals,On the abstract Cauchy problem, J. Func. Anal.10 (1972), 281–299.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    P. Brenner,The Cauchy problem for symmetric hyperbolic systems in L p Math. Scand.19 (1966), 27–37.MATHMathSciNetGoogle Scholar
  6. [6]
    G. Chen, D.L. Russell,A mathematical model for linear elastic systems with structural damping, Quart. Appl. Math. (1982), 433–454.Google Scholar
  7. [7]
    I. Ciorąnescu,On the abstract Cauchy problem for the operator d 2 /dt 2 −A, Integral Equations Operator Theory7 (1984), 27–35.CrossRefMathSciNetMATHGoogle Scholar
  8. [8]
    G. Da Prato,Semigruppi regolarizzabili, Ricerche Mat.15 (1966), 223–246.MATHMathSciNetGoogle Scholar
  9. [9]
    E.B. Davies and M.M. Pang,The Cauchy problem and a generalization of the Hille-Yosida Theorem, Proc. London Math. Soc.55 (1987), 181–208.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    R. deLaubenfels,The relationship between C-semigroups and integrated semigroups, Preprint 1988.Google Scholar
  11. [11]
    R. deLaubenfels,C-semigroups and the Cauchy problem, Preprint 1988.Google Scholar
  12. [12]
    K. Engel,Polynomial operator matrices, Dissertation, Univ. Tübingen 1988.Google Scholar
  13. [13]
    H. Engler, F. Neubrander, J. Sandefur,Second order strongly damped quasilinear equations, In: T.L. Gill, W.W. Zachary (eds.). “Nonlinear Semigroups, Partial Differential Equations and Attractors,” Lecture Notes1248, Springer-Verlag, 1987.Google Scholar
  14. [14]
    H. Falun, L. Kangsheng,On the mathematical model for linear elastic systems with structural damping, Preprint 1987.Google Scholar
  15. [15]
    H.O. Fattorini, “The Cauchy Problem,” Addison Wesley, Reading, Mass., 1983.MATHGoogle Scholar
  16. [16]
    H.O. Fattorini, “Second Order Linear Differential Equations in Banach Spaces,” North-Holland Mathematics Studies108, 1985.Google Scholar
  17. [17]
    J.A. Goldstein, “Semigroups of Linear Operators and Applications,” Oxford University Press, New York, 1985.MATHGoogle Scholar
  18. [18]
    R. Hersh,Explicit solutions of a class of higher order abstract Cauchy problems, J. Diff. Eqns.8 (1970), 570–579.MATHCrossRefMathSciNetGoogle Scholar
  19. [19]
    M. Hieber, Dissertation, Univ. Tübingen. To appear.Google Scholar
  20. [20]
    H. Kellermann,Integrated semigroups, Dissertation, Univ. Tübingen, 1986.Google Scholar
  21. [21]
    J. Kisynski,On cosine operator functions and one-parameter groups of operators, Studia Math.44 (1972), 93–105.MathSciNetGoogle Scholar
  22. [22]
    J.L. Lions,Les semi-groupes distributions, Portugaliae Mathematica19 (1960), 141–164.MATHMathSciNetGoogle Scholar
  23. [23]
    W. Littman,The wave operator and L p norms, J. Math. Mech.12 (1963), 55–68.MATHMathSciNetGoogle Scholar
  24. [24]
    I. Miyadera,On the generators of exponentially bounded C-semigroups, Proc. Japan Acad.62 (1986), 239–242.MATHMathSciNetGoogle Scholar
  25. [25]
    I. Miyadera, S. Oharu, and N. Okazawa,Generation theorems of semigroups of linear operators, Publ. Res. Inst. Math. Sci., Kyoto Univ.8 (1973), 509–555.MathSciNetGoogle Scholar
  26. [26]
    I.V. Mel’nikova, A.I. Filinkoy,Classification and well-posedness of the Cauchy problem for second-order equations in a Banach space, Soviet Math. Dokl.29 (1984), 646–651.MATHGoogle Scholar
  27. [27]
    R. Nagel,Towards a “matrix theory” for unbounded operator matries, Math. Z. To appear.Google Scholar
  28. [28]
    F. Neubrander,Wellposedness of higher order abstract Cauchy problems, Trans. Amer. Math. Soc.295 (1986), 257–290.MATHCrossRefMathSciNetGoogle Scholar
  29. [29]
    F. Neubrander,Integrated semigroups and their applications to the abstract Cauchy problem, Pacific J. Math. To appear.Google Scholar
  30. [30]
    E. Obrecht,Sul problema di Cauchy per le equazioni paraboliche astratte di ordine n, Rend. Sem. Mat. Univ. Padova,53 (1975), 231–256.MathSciNetGoogle Scholar
  31. [31]
    J. Sandefur,Existence and Uniqueness of solutions of second order nonlinear differential equations, SIAM J. Math. Anal.14 (1983), 477–487.MATHCrossRefMathSciNetGoogle Scholar
  32. [32]
    M. Sova,Probleme de Cauchy pour equations hyperboliques operation-nelles a coefficients constants non-bornes, Ann. Scuola Norm. Suo. Pisa,22 (1968), 67–100.MATHMathSciNetGoogle Scholar
  33. [33]
    M. Sova,Problemes de Cauchy paraboliques abstraits de classes superieures et les semi-groupes distributions, Ricerche Mat.18 (1969), 215–238.MATHMathSciNetGoogle Scholar
  34. [34]
    T. Takenaka, N. Okazawa,Abstract Cauchy problems for second order linear differential equations in a Banach space, Hiroshima Math. J.17 (1987), 591–612.MATHMathSciNetGoogle Scholar
  35. [35]
    N. Tanaka,On exponentially bounded C-semigroups, Tokyo J. Math.10 (1987), 107–117.MATHMathSciNetCrossRefGoogle Scholar
  36. [36]
    N. Tanaka, I. Miyadera,Some remarks on C-semigroups and integrated semigroups, Proc. Japan Acad.63 (1987), 139–142.MATHMathSciNetGoogle Scholar
  37. [37]
    H.R. Thieme,Integrated semigroups and duality, Preprint 1987.Google Scholar
  38. [38]
    C.C. Travis, G.F. Webb,Cosine families and abstract nonlinear second order differential equations, Acta Math. Sci. Hung.32 (1978), 75–96.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag New York Inc 1989

Authors and Affiliations

  • Frank Neubrander
    • 1
    • 2
  1. 1.Mathematische FakultätUniversität TübingenTübingenFRG
  2. 2.Department of MathematicsGeorgetown UniversityWashington, DCUSA

Personalised recommendations