A Cauchy problem for an abstract nonlinear Volterra integrodifferential equation is considered. Existence and uniqueness results are shown for any given time interval under weak time regularity assumptions on the kernel. Some applications to the heat flow with memory are presented.
Si studia un problema di Cauchy per un'equazione integrodifferenziale astratta nonlineare di Volterra. Si provano risultati di esistenza e unicità supponendo il nucleo debolmente regolare rispetto al tempo. Si presentano alcune applicazioni dei risultati ottenuti a modelli di conduzione del calore con memoria.
@article{RLIN_1991_9_2_1_43_0,
author = {Maurizio Grasselli and Alfredo Lorenzi},
title = {Abstract nonlinear Volterra integrodifferential equations with nonsmooth kernels},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
volume = {2},
year = {1991},
pages = {43-53},
zbl = {0819.45006},
mrnumber = {1120122},
language = {en},
url = {http://dml.mathdoc.fr/item/RLIN_1991_9_2_1_43_0}
}
Grasselli, Maurizio; Lorenzi, Alfredo. Abstract nonlinear Volterra integrodifferential equations with nonsmooth kernels. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 2 (1991) pp. 43-53. http://gdmltest.u-ga.fr/item/RLIN_1991_9_2_1_43_0/
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