Existence and uniqueness for an integro-differential equation with singular kernel
Berti, Valeria
Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006), p. 299-309 / Harvested from 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 L1-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.

In questo articolo si studia un problema evolutivo per la viscoelasticità lineare, supponendo che il nucleo di memoria G′ sia singolare. Si assume che G′ presenti una singolarità iniziale in modo che non sia una funzione L1 nel tempo, ma che la funzione G sia integrabile per t=0. Applicando il metodo delle trasformate di Fourier, si dimostra un teorema di esistenza e unicità della soluzione debole, in un opportuno spazio funzionale, la cui definizione dipende esplicitamente dalle proprietà del nucleo di memoria.

Publié le : 2006-06-01
@article{BUMI_2006_8_9B_2_299_0,
     author = {Valeria Berti},
     title = {Existence and uniqueness for an integro-differential equation with singular kernel},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {9-A},
     year = {2006},
     pages = {299-309},
     zbl = {1178.45011},
     mrnumber = {2233139},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2006_8_9B_2_299_0}
}

Berti, Valeria. Existence and uniqueness for an integro-differential equation with singular kernel. Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006) pp. 299-309. http://gdmltest.u-ga.fr/item/BUMI_2006_8_9B_2_299_0/

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