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Integrated semigroups and their application to complete second order cauchy problems

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References

  1. W. Arendt,Vector valued Lrplace transforms and Cauchy problems, Israel J. Math.59 (1987), 327–352.

    MATH  MathSciNet  Google Scholar 

  2. W. Arendt, H. Kellermann,Integrated solutions of Volterra integro-differential equations and applications, Preprint 1987.

  3. P. Aviles, J. Sandefur,Nonlinear second order equations with applications to partial differential equations, J. Diff. Eqns.58 (1985), 404–427.

    Article  MATH  MathSciNet  Google Scholar 

  4. R. Beals,On the abstract Cauchy problem, J. Func. Anal.10 (1972), 281–299.

    Article  MATH  MathSciNet  Google Scholar 

  5. P. Brenner,The Cauchy problem for symmetric hyperbolic systems in L p Math. Scand.19 (1966), 27–37.

    MATH  MathSciNet  Google Scholar 

  6. G. Chen, D.L. Russell,A mathematical model for linear elastic systems with structural damping, Quart. Appl. Math. (1982), 433–454.

  7. I. Ciorąnescu,On the abstract Cauchy problem for the operator d 2 /dt 2 −A, Integral Equations Operator Theory7 (1984), 27–35.

    Article  MathSciNet  MATH  Google Scholar 

  8. G. Da Prato,Semigruppi regolarizzabili, Ricerche Mat.15 (1966), 223–246.

    MATH  MathSciNet  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  10. R. deLaubenfels,The relationship between C-semigroups and integrated semigroups, Preprint 1988.

  11. R. deLaubenfels,C-semigroups and the Cauchy problem, Preprint 1988.

  12. K. Engel,Polynomial operator matrices, Dissertation, Univ. Tübingen 1988.

  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.

  14. H. Falun, L. Kangsheng,On the mathematical model for linear elastic systems with structural damping, Preprint 1987.

  15. H.O. Fattorini, “The Cauchy Problem,” Addison Wesley, Reading, Mass., 1983.

    MATH  Google Scholar 

  16. H.O. Fattorini, “Second Order Linear Differential Equations in Banach Spaces,” North-Holland Mathematics Studies108, 1985.

  17. J.A. Goldstein, “Semigroups of Linear Operators and Applications,” Oxford University Press, New York, 1985.

    MATH  Google Scholar 

  18. R. Hersh,Explicit solutions of a class of higher order abstract Cauchy problems, J. Diff. Eqns.8 (1970), 570–579.

    Article  MATH  MathSciNet  Google Scholar 

  19. M. Hieber, Dissertation, Univ. Tübingen. To appear.

  20. H. Kellermann,Integrated semigroups, Dissertation, Univ. Tübingen, 1986.

  21. J. Kisynski,On cosine operator functions and one-parameter groups of operators, Studia Math.44 (1972), 93–105.

    MathSciNet  Google Scholar 

  22. J.L. Lions,Les semi-groupes distributions, Portugaliae Mathematica19 (1960), 141–164.

    MATH  MathSciNet  Google Scholar 

  23. W. Littman,The wave operator and L p norms, J. Math. Mech.12 (1963), 55–68.

    MATH  MathSciNet  Google Scholar 

  24. I. Miyadera,On the generators of exponentially bounded C-semigroups, Proc. Japan Acad.62 (1986), 239–242.

    MATH  MathSciNet  Google Scholar 

  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.

    MathSciNet  Google Scholar 

  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.

    MATH  Google Scholar 

  27. R. Nagel,Towards a “matrix theory” for unbounded operator matries, Math. Z. To appear.

  28. F. Neubrander,Wellposedness of higher order abstract Cauchy problems, Trans. Amer. Math. Soc.295 (1986), 257–290.

    Article  MATH  MathSciNet  Google Scholar 

  29. F. Neubrander,Integrated semigroups and their applications to the abstract Cauchy problem, Pacific J. Math. To appear.

  30. E. Obrecht,Sul problema di Cauchy per le equazioni paraboliche astratte di ordine n, Rend. Sem. Mat. Univ. Padova,53 (1975), 231–256.

    MathSciNet  Google Scholar 

  31. J. Sandefur,Existence and Uniqueness of solutions of second order nonlinear differential equations, SIAM J. Math. Anal.14 (1983), 477–487.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    MATH  MathSciNet  Google Scholar 

  33. M. Sova,Problemes de Cauchy paraboliques abstraits de classes superieures et les semi-groupes distributions, Ricerche Mat.18 (1969), 215–238.

    MATH  MathSciNet  Google Scholar 

  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.

    MATH  MathSciNet  Google Scholar 

  35. N. Tanaka,On exponentially bounded C-semigroups, Tokyo J. Math.10 (1987), 107–117.

    Article  MATH  MathSciNet  Google Scholar 

  36. N. Tanaka, I. Miyadera,Some remarks on C-semigroups and integrated semigroups, Proc. Japan Acad.63 (1987), 139–142.

    MATH  MathSciNet  Google Scholar 

  37. H.R. Thieme,Integrated semigroups and duality, Preprint 1987.

  38. C.C. Travis, G.F. Webb,Cosine families and abstract nonlinear second order differential equations, Acta Math. Sci. Hung.32 (1978), 75–96.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Mathematische Fakultät, Universität Tübingen, Auf der Morgenstelle 10, 7400, Tübingen, FRG

    Frank Neubrander

  2. Department of Mathematics, Georgetown University, 20057, Washington, DC, USA

    Frank Neubrander

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  1. Frank Neubrander
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This research was supported by the NSF through grant DMS-8601983

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Neubrander, F. Integrated semigroups and their application to complete second order cauchy problems. Semigroup Forum 38, 233–251 (1989). https://doi.org/10.1007/BF02573234

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