On a large class of kernels yielding exponential stability in viscoelasticity

Nasser eddine Tatar

doi:10.1016/j.amc.2009.08.034

On a large class of kernels yielding exponential stability in viscoelasticity

Nasser eddine Tatar^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

In this paper we prove exponential decay of solutions for a problem which appears in viscoelasticity. The conditions on the admissible kernels are relaxed so as to allow for more kernels to be treated. Namely, the smallness of the kernels is replaced by the smallness of the set where the kernel is flat. This work extends previous works and improves in particular a recent result by Pata [16]. This is established by introducing two lemmas, an idea due to Pata and using the energy method.

Original language	English
Pages (from-to)	2298-2306
Number of pages	9
Journal	Applied Mathematics and Computation
Volume	215
Issue number	6
DOIs	https://doi.org/10.1016/j.amc.2009.08.034
State	Published - 15 Nov 2009

Bibliographical note

Funding Information:
The author is grateful for the financial support and the facilities provided by King Fahd University of Petroleum and Minerals through the Grant SB070013 .

Keywords

Exponential decay
Memory term
Relaxation function
Viscoelasticity

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2009.08.034

Cite this

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title = "On a large class of kernels yielding exponential stability in viscoelasticity",

abstract = "In this paper we prove exponential decay of solutions for a problem which appears in viscoelasticity. The conditions on the admissible kernels are relaxed so as to allow for more kernels to be treated. Namely, the smallness of the kernels is replaced by the smallness of the set where the kernel is flat. This work extends previous works and improves in particular a recent result by Pata [16]. This is established by introducing two lemmas, an idea due to Pata and using the energy method.",

keywords = "Exponential decay, Memory term, Relaxation function, Viscoelasticity",

author = "Tatar, \{Nasser eddine\}",

note = "Funding Information: The author is grateful for the financial support and the facilities provided by King Fahd University of Petroleum and Minerals through the Grant SB070013 .",

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T1 - On a large class of kernels yielding exponential stability in viscoelasticity

AU - Tatar, Nasser eddine

N1 - Funding Information: The author is grateful for the financial support and the facilities provided by King Fahd University of Petroleum and Minerals through the Grant SB070013 .

PY - 2009/11/15

Y1 - 2009/11/15

N2 - In this paper we prove exponential decay of solutions for a problem which appears in viscoelasticity. The conditions on the admissible kernels are relaxed so as to allow for more kernels to be treated. Namely, the smallness of the kernels is replaced by the smallness of the set where the kernel is flat. This work extends previous works and improves in particular a recent result by Pata [16]. This is established by introducing two lemmas, an idea due to Pata and using the energy method.

AB - In this paper we prove exponential decay of solutions for a problem which appears in viscoelasticity. The conditions on the admissible kernels are relaxed so as to allow for more kernels to be treated. Namely, the smallness of the kernels is replaced by the smallness of the set where the kernel is flat. This work extends previous works and improves in particular a recent result by Pata [16]. This is established by introducing two lemmas, an idea due to Pata and using the energy method.

KW - Exponential decay

KW - Memory term

KW - Relaxation function

KW - Viscoelasticity

UR - https://www.scopus.com/pages/publications/70350001130

U2 - 10.1016/j.amc.2009.08.034

DO - 10.1016/j.amc.2009.08.034

M3 - Article

AN - SCOPUS:70350001130

SN - 0096-3003

VL - 215

SP - 2298

EP - 2306

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 6

ER -

On a large class of kernels yielding exponential stability in viscoelasticity

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Cite this