On relatively bounded perturbations of linear C 0 -semigroups

W. Desch; W. Schappacher

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1984)

  • Volume: 11, Issue: 2, page 327-341
  • ISSN: 0391-173X

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Desch, W., and Schappacher, W.. "On relatively bounded perturbations of linear $C_0$-semigroups." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 11.2 (1984): 327-341. <http://eudml.org/doc/83934>.

@article{Desch1984,
author = {Desch, W., Schappacher, W.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {linear abstract Cauchy problem; -semigroup; relative boundedness; ultimately differentiable; semigroup settings for functional differential equations; abstract Volterra integrodifferential equations},
language = {eng},
number = {2},
pages = {327-341},
publisher = {Scuola normale superiore},
title = {On relatively bounded perturbations of linear $C_0$-semigroups},
url = {http://eudml.org/doc/83934},
volume = {11},
year = {1984},
}

TY - JOUR
AU - Desch, W.
AU - Schappacher, W.
TI - On relatively bounded perturbations of linear $C_0$-semigroups
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1984
PB - Scuola normale superiore
VL - 11
IS - 2
SP - 327
EP - 341
LA - eng
KW - linear abstract Cauchy problem; -semigroup; relative boundedness; ultimately differentiable; semigroup settings for functional differential equations; abstract Volterra integrodifferential equations
UR - http://eudml.org/doc/83934
ER -

References

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  1. [1] J. Ball, Strongly continuous semigroups, weak solutions and the variation of constants formula, Proc. Amer. Math. Soc., 63 (1977), pp. 370-373. Zbl0353.47017MR442748
  2. [2] H. Brezis, Operateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert, North Holland (1973). Zbl0252.47055
  3. [3] G. Chen - R. Grimmer, Semigroups and integral equations, J. Integral Equations, 2 (1980), pp. 133-154. Zbl0449.45007MR572484
  4. [4] G. Da Prato - P. Grisvard, Equations d'evolution abstraites non lineaires de type parabolique, Annali Mat. Pura ed Appl., 70 (1979), pp. 329-396. Zbl0471.35036MR551075
  5. [5] M.C. Delfour, The largest class of hereditary systems defining a C0-semigroup on the product space, Canad. J. Math., 32 (1980), pp. 969-978. Zbl0448.34074MR590659
  6. [6] P. Hess, Zur Störungstheorie linearer Operatoren: Relative Beschränktheit und relative Kompaktheit von Operatoren in Banachräumen, Comm. Math. Helv., 44 (1969), pp. 245-248. Zbl0181.13705MR246156
  7. [7] F. Kappel - W. Schappacher, Nonlinear functional differential equations and abstract integral equations, Proc. Royal Soc. Edinburgh, 84A (1979), pp. 71-91. Zbl0455.34057MR549872
  8. [8] T. Kato, Perturbation Theory for Linear Operators, Springer (1976). Zbl0342.47009MR407617
  9. [9] K. Kunisch and W. Schappacher, Necessary conditions for partial differential equations with delay to generate C0-semigroups, J. Differential Equations, 50 (1983), pp. 49-79. Zbl0533.35082MR717868
  10. [10] R. Miller, Volterra integral equations in a Banach space, Funkcial. Ekvac., 18 (1975), pp. 163-193. Zbl0326.45007MR410312
  11. [11] J. Zabczyk, A semigroup approach to boundary value control, in Proc. of the 2nd IFAC Symposium on Control of distributed parameter systems (S. Banks, A. Pritchard eds.), pp. 99-107. Zbl0398.93028MR534864
  12. [12] J. Zabczyk, On decomposition of generators, SIAM. J. Control and Optimization, 16 (1978), pp. 523-534. Zbl0393.93023MR512915

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