Linear abstract integro-differential equations of hyperbolic type in Hilbert spaces

G. Da Prato; M. Iannelli

Rendiconti del Seminario Matematico della Università di Padova (1980)

  • Volume: 62, page 191-206
  • ISSN: 0041-8994

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Da Prato, G., and Iannelli, M.. "Linear abstract integro-differential equations of hyperbolic type in Hilbert spaces." Rendiconti del Seminario Matematico della Università di Padova 62 (1980): 191-206. <http://eudml.org/doc/107744>.

@article{DaPrato1980,
author = {Da Prato, G., Iannelli, M.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {hyperbolic type; existence; Hilbert space},
language = {eng},
pages = {191-206},
publisher = {Seminario Matematico of the University of Padua},
title = {Linear abstract integro-differential equations of hyperbolic type in Hilbert spaces},
url = {http://eudml.org/doc/107744},
volume = {62},
year = {1980},
}

TY - JOUR
AU - Da Prato, G.
AU - Iannelli, M.
TI - Linear abstract integro-differential equations of hyperbolic type in Hilbert spaces
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1980
PB - Seminario Matematico of the University of Padua
VL - 62
SP - 191
EP - 206
LA - eng
KW - hyperbolic type; existence; Hilbert space
UR - http://eudml.org/doc/107744
ER -

References

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  1. [1] V. Barbu, Nonlinear Volterra equations in a Hilbert space, SIAM J. Math. Anal., 6 (1975), pp. 728-741. Zbl0322.45012MR377620
  2. [2] V. Barbu, Nonlinear Volterra integro-differential equations in Hilbert space, Sem. Mat. Bari, 143 (1976). Zbl0365.45001
  3. [3] H. Brézis, Opérateurs maximaux monotones et sémi-groupes de contractions dans les espaces de Hilbert, Math. Studies, 5, North Holland (1973). Zbl0252.47055MR348562
  4. [4] M.G. Crandall - S.O. Londen - J.A. Nohel, An abstract nonlinear Volterra integro-differential equation, J. Math. Anal. Appl., 64 (1978), pp. 701-735. Zbl0395.45023MR500052
  5. [5] C.M. Dafermos, An abstract Volterra equation with applications to linear viscoelasticity, J. Diff. Eq., 7 (1970), pp. 554-569. Zbl0212.45302MR259670
  6. [6] C.M. Dafermos - J.A. Nohel, Energy methods for nonlinearhyperbolic integro-differential equations, Comm. PDE, 4 (1979), pp. 219-278. Zbl0464.45009MR522712
  7. [7] G. Da Prato - P. Grisvard, Sommes d'opérateurs linéaires et équations differentielles opérationnelles, J. Math. Pures et Appl., 54 (1975), pp. 305-387. Zbl0315.47009MR442749
  8. [8] G. Da Prato - M. Iannelli, On a method to study abstract evolution equations in the hyperbolic case, Comm. PDE, 1 (1976), pp. 585-608. Zbl0358.34063MR442750
  9. [9] G. Da Prato - M. Iannelli, Linear integro-differential equations in Banach spaces, Rend. Sem. Mat. Padova, 62 (1980), pp. 207-219. Zbl0451.45014MR582951
  10. [10] S.O. Londen, On an integral equation in a Hilbert space, SIAM J. Math. Anal., 8 (1977), pp. 950-970. Zbl0379.45011MR511229
  11. [11] S.O. Londen, On an integro-differential Volterra equation with a maximal monotone mapping, J. Diff. Eq., 27 (1978), pp. 405-420. Zbl0364.45003MR499976
  12. [12] R.C. Mac Camy, Approximations for a class of functional differential equations, SIAM J. Appl. Math., 23 (1972), pp. 70-83. Zbl0237.34102
  13. [13] R.C. Mac Camy, Stability theorems for a class of functional differential equations, SIAM J. Appl. Math., 30 (1976), pp. 557-576. Zbl0346.34059MR404818
  14. [14] R.C. Mac Camy - J.S.W. Wong, Stability theorems for some functiona. equations, Trans. AMS, 164 (1972), pp. 1-37. Zbl0274.45012MR293355
  15. [15] R.K. Miller - R. L. WHEELER, Asymptotic behavior for a linear Volterra integral equation in Hilbert space, J. Diff. Eq., 23 (1977), pp. 270-284. Zbl0341.45017MR440313

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