# Existence and uniqueness for an integro-differential equation with singular kernel

Bollettino dell'Unione Matematica Italiana (2006)

- Volume: 9-B, Issue: 2, page 299-309
- ISSN: 0392-4033

## Access Full Article

top## Abstract

top## How to cite

topBerti, Valeria. "Existence and uniqueness for an integro-differential equation with singular kernel." Bollettino dell'Unione Matematica Italiana 9-B.2 (2006): 299-309. <http://eudml.org/doc/289611>.

@article{Berti2006,

abstract = {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.},

author = {Berti, Valeria},

journal = {Bollettino dell'Unione Matematica Italiana},

language = {eng},

month = {6},

number = {2},

pages = {299-309},

publisher = {Unione Matematica Italiana},

title = {Existence and uniqueness for an integro-differential equation with singular kernel},

url = {http://eudml.org/doc/289611},

volume = {9-B},

year = {2006},

}

TY - JOUR

AU - Berti, Valeria

TI - Existence and uniqueness for an integro-differential equation with singular kernel

JO - Bollettino dell'Unione Matematica Italiana

DA - 2006/6//

PB - Unione Matematica Italiana

VL - 9-B

IS - 2

SP - 299

EP - 309

AB - 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.

LA - eng

UR - http://eudml.org/doc/289611

ER -

## References

top- FABRIZIO, M. - LAZZARI, B., On the existence and asymptotic stability of solutions for linearly viscoelastic solids, Arch. Rational Mech. Anal., 116 (2) (1991), 139-152. Zbl0766.73013
- FABRIZIO, M. - LAZZARI, B., The domain of dependence inequality and asymptotic stability for a viscoelastic solid, Nonlinear Oscil., 1 (1998), 117-133. Zbl1071.74587
- FABRIZIO, M. - MORRO, A., Mathematical problems in linear viscoelasticity, SIAM, Philadelphia, 1992. Zbl0753.73003
- GENTILI, G., Regularity and stability for a viscoelastic material with a singular memory kernel, J. Elasticity, 37 (2) (1995), 139-156. Zbl0818.73026
- HANYGA, A., Wave propagation in media with singular memory, Math. Comput. Modelling, 34 (12-13) (2001), 1329-1421. Zbl1011.74033
- HRUSA, W.J. - RENARDY, M., On wave propagation in linear viscoelasticity, Quart. Appl. Math., 43 (2) (1985), 237-254. Zbl0571.73026
- LADYZHENSKAYA, O. A., The boundary value problem of mathematical physics, Springer, New York, 1985. Zbl0588.35003
- RENARDY, M. - HRUSA, W. J. - NOHEL, J. A., Mathematical problems in viscoelasticity, Longman Scientific & Technical, John Wiley & Sons, New York, 1987.
- SHOWALTER, R. E., Hilbert space methods for differential equations, Pitman, London, 1977. Zbl0364.35001
- TREVES, F., Basic linear partial differential equations, Acad. press, New York, 1975. Zbl0305.35001

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.