# Decay rates of Volterra equations on ℝN

Monica Conti; Stefania Gatti; Vittorino Pata

Open Mathematics (2007)

- Volume: 5, Issue: 4, page 720-732
- ISSN: 2391-5455

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topMonica Conti, Stefania Gatti, and Vittorino Pata. "Decay rates of Volterra equations on ℝN." Open Mathematics 5.4 (2007): 720-732. <http://eudml.org/doc/269324>.

@article{MonicaConti2007,

abstract = {This note is concerned with the linear Volterra equation of hyperbolic type \[\partial \_\{tt\} u(t) - \alpha \Delta u(t) + \int \_0^t \{\mu (s)\Delta u(t - s)\} ds = 0\]
on the whole space ℝN. New results concerning the decay of the associated energy as time goes to infinity were established.},

author = {Monica Conti, Stefania Gatti, Vittorino Pata},

journal = {Open Mathematics},

keywords = {Integro-differential equations; memory kernel; polynomial decay; decay of energy},

language = {eng},

number = {4},

pages = {720-732},

title = {Decay rates of Volterra equations on ℝN},

url = {http://eudml.org/doc/269324},

volume = {5},

year = {2007},

}

TY - JOUR

AU - Monica Conti

AU - Stefania Gatti

AU - Vittorino Pata

TI - Decay rates of Volterra equations on ℝN

JO - Open Mathematics

PY - 2007

VL - 5

IS - 4

SP - 720

EP - 732

AB - This note is concerned with the linear Volterra equation of hyperbolic type \[\partial _{tt} u(t) - \alpha \Delta u(t) + \int _0^t {\mu (s)\Delta u(t - s)} ds = 0\]
on the whole space ℝN. New results concerning the decay of the associated energy as time goes to infinity were established.

LA - eng

KW - Integro-differential equations; memory kernel; polynomial decay; decay of energy

UR - http://eudml.org/doc/269324

ER -

## References

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- [12] V. Pata: “Exponential stability in linear viscoelasticity”, Quart. Appl. Math., Vol. 64, (2006), pp. 499–513. Zbl1117.35052
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