On a perturbed kernel in viscoelasticity

Nasser Eddine Tatar

doi:10.1016/j.aml.2010.12.035

On a perturbed kernel in viscoelasticity

Nasser Eddine Tatar^*

^*Corresponding author for this work

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

11 Scopus citations

Abstract

For a viscoelastic problem we consider a kernel satisfying the standard condition (the derivative of the kernel is smaller than or equal to a negative constant times the kernel itself) yielding exponential decay of the solutions. We perturb this relaxation function in such a manner that the standard condition is no longer satisfied (for any constant). It is proved that we still have exponential decay in the case where the L1-norm of the perturbation is small enough.

Original language	English
Pages (from-to)	766-770
Number of pages	5
Journal	Applied Mathematics Letters
Volume	24
Issue number	5
DOIs	https://doi.org/10.1016/j.aml.2010.12.035
State	Published - May 2011

Bibliographical note

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

Keywords

Exponential decay
Memory term
Relaxation function
Viscoelasticity

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aml.2010.12.035

Cite this

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title = "On a perturbed kernel in viscoelasticity",

abstract = "For a viscoelastic problem we consider a kernel satisfying the standard condition (the derivative of the kernel is smaller than or equal to a negative constant times the kernel itself) yielding exponential decay of the solutions. We perturb this relaxation function in such a manner that the standard condition is no longer satisfied (for any constant). It is proved that we still have exponential decay in the case where the L1-norm of the perturbation is small enough.",

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

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

PY - 2011/5

Y1 - 2011/5

N2 - For a viscoelastic problem we consider a kernel satisfying the standard condition (the derivative of the kernel is smaller than or equal to a negative constant times the kernel itself) yielding exponential decay of the solutions. We perturb this relaxation function in such a manner that the standard condition is no longer satisfied (for any constant). It is proved that we still have exponential decay in the case where the L1-norm of the perturbation is small enough.

AB - For a viscoelastic problem we consider a kernel satisfying the standard condition (the derivative of the kernel is smaller than or equal to a negative constant times the kernel itself) yielding exponential decay of the solutions. We perturb this relaxation function in such a manner that the standard condition is no longer satisfied (for any constant). It is proved that we still have exponential decay in the case where the L1-norm of the perturbation is small enough.

KW - Exponential decay

KW - Memory term

KW - Relaxation function

KW - Viscoelasticity

UR - https://www.scopus.com/pages/publications/79551477575

U2 - 10.1016/j.aml.2010.12.035

DO - 10.1016/j.aml.2010.12.035

M3 - Article

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SN - 0893-9659

VL - 24

SP - 766

EP - 770

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 5

ER -

On a perturbed kernel in viscoelasticity

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this