On a class of second order integrodifferential equations

Daniela Sforza

Rendiconti del Seminario Matematico della Università di Padova (1991)

  • Volume: 86, page 157-174
  • ISSN: 0041-8994

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Sforza, Daniela. "On a class of second order integrodifferential equations." Rendiconti del Seminario Matematico della Università di Padova 86 (1991): 157-174. <http://eudml.org/doc/108230>.

@article{Sforza1991,
author = {Sforza, Daniela},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {Banach space; Laplace transformable functions; resolvent operator; existence; uniqueness; strict and strong solutions; abstract second order integrodifferential equation; analytic semigroup; variation of constants formula},
language = {eng},
pages = {157-174},
publisher = {Seminario Matematico of the University of Padua},
title = {On a class of second order integrodifferential equations},
url = {http://eudml.org/doc/108230},
volume = {86},
year = {1991},
}

TY - JOUR
AU - Sforza, Daniela
TI - On a class of second order integrodifferential equations
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1991
PB - Seminario Matematico of the University of Padua
VL - 86
SP - 157
EP - 174
LA - eng
KW - Banach space; Laplace transformable functions; resolvent operator; existence; uniqueness; strict and strong solutions; abstract second order integrodifferential equation; analytic semigroup; variation of constants formula
UR - http://eudml.org/doc/108230
ER -

References

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  1. [1] C.M. Dafermos, An abstract Volterra equation with applications to linear viscoelasticity, J. Diff. Eq., 7 (1970), pp. 554-569. Zbl0212.45302MR259670
  2. [2] C.M. Dafermos, Asymptotic stability in viscoelasticity, Arch. Rat. Mech. Anal., 37 (1970), pp. 297-308. Zbl0214.24503MR281400
  3. [3] C.M. Dafermos - J.A. Nohel, Energy methods for nonlinear hyperbolic Volterra integrodifferential equations, Comm. Part. Diff. Eq., 4 (3) (1979), pp. 219-278. Zbl0464.45009MR522712
  4. [4] C.M. Dafermos - J.A. Nohel, A nonlinear hyperbolic Volterra equation in viscoelasticity, Amer. J. Math. Supplement (1981), pp. 87-116. Zbl0588.35016MR648457
  5. [5] G. Da Prato - M. Iannelli, Linear integro-differential equations in Banach spaces, Rend. Sem. Mat. Univ. Padova, 62 (1980), pp. 207-219. Zbl0451.45014MR582951
  6. [6] G. Da Prato - M. Iannelli - E. Sinestrari, Temporal regularity for a class of integrodifferential equations in Banach spaces, Boll. U. M. I. Anal. Funz. Appl. Serie VI, Vol. II-C, N. 1 (1983), pp. 171-185. Zbl0527.45005MR718369
  7. [7] G. Da Prato - M. Iannelli - E. Sinestrari, Regularity of solutions of a class of linear integrodifferential equations in Banach spaces, J. Int. Eq., 8 (1985), pp. 27-40. Zbl0576.45011MR771750
  8. [8] G. Da Prato - M. Iannelli, Existence and regularity for a class of integrodifferential equations of parabolic type, J. Math. Anal. Appl., 112 (1985), pp. 36-55. Zbl0583.45009MR812792
  9. [9] G. Da Prato - A. Lunardi, Solvability on the real line of a class of linear Volterra integrodifferential equations of parabolic type, Ann. Mat. Pura Appl. (IV), CL (1988), pp. 67-118. Zbl0646.45013MR946030
  10. [10] W.J. Hrusa - J.A. Nohel, The Cauchy problem in one-dimensional nonlinear viscoelasticity, J. Diff. Eq., 59 (1985), pp. 388-412. Zbl0535.35057MR807854
  11. [11] W.J. Hrusa - M. Renardy - J.A. Nohel, Mathematical Problems in Viscoelasticity, Longman Group Limited. Zbl0719.73013
  12. [12] A. Lunardi, Laplace transform methods in integrodifferential equations, J. Int. Eq., 10 (1985), pp. 185-211. Zbl0587.45015MR831244
  13. [13] R.C. Maccamy, A model for one-dimensional, nonlinear viscoelasticity, Q. Appl. Math., 35 (1977), pp. 21-33. Zbl0355.73041MR478939
  14. [14] D.V. Widder, TheLaplace Transform, Princeton University Press, Princeton (1941). Zbl0063.08245MR5923

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