Geodesic
Existence and uniqueness for an integro-differential equation with singular kernel
Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 2, pp. 299-309 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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In this paper we study the evolutive problem of linear viscoelasticity with a singular kernel memory $G'$. We assume that $G'$ presents an initial singularity, so that it is not a $L^1$-function in time, whereas the relaxation function $G$ is integrable at $t = 0$. By applying the Fourier transform method, we prove a theorem of existence and uniqueness of the weak solutions in a functional space whose definition is strictly related to the properties of the kernel memory. 
@article{BUMI_2006_8_9B_2_a3,
     author = {Berti, Valeria},
     title = {Existence and uniqueness for an integro-differential equation with singular kernel},
     journal = {Bollettino della Unione matematica italiana},
     pages = {299--309},
     year = {2006},
     volume = {Ser. 8, 9B},
     number = {2},
     zbl = {1178.45011},
     mrnumber = {MR2233139},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_2_a3/}
}
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Berti, Valeria. Existence and uniqueness for an integro-differential equation with singular kernel. Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 2, pp. 299-309. http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_2_a3/