On a non-dissipative Kirchhoff viscoelastic problem

N. Tatar

doi:10.3103/S1068362313060058

On a non-dissipative Kirchhoff viscoelastic problem

N. Tatar^*

^*Corresponding author for this work

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

3 Scopus citations

Abstract

In this paper we consider a Kirchhoff type viscoelastic problem, and prove uniform stability of the system. We do not rely on the dissipativity of the system or the boundedness of the energy as in the previous treatments. There appears a quadratic term which we cannot estimate by the initial energy as our system is not clearly dissipative in advance.

Original language	English
Pages (from-to)	285-296
Number of pages	12
Journal	Journal of Contemporary Mathematical Analysis
Volume	48
Issue number	6
DOIs	https://doi.org/10.3103/S1068362313060058
State	Published - 2013

Bibliographical note

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

Keywords

Exponential decay
Kirchhoff equation
memory term
relaxation function
viscoelasticity

ASJC Scopus subject areas

Analysis
Control and Optimization
Applied Mathematics

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10.3103/S1068362313060058

Cite this

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title = "On a non-dissipative Kirchhoff viscoelastic problem",

abstract = "In this paper we consider a Kirchhoff type viscoelastic problem, and prove uniform stability of the system. We do not rely on the dissipativity of the system or the boundedness of the energy as in the previous treatments. There appears a quadratic term which we cannot estimate by the initial energy as our system is not clearly dissipative in advance.",

keywords = "Exponential decay, Kirchhoff equation, memory term, relaxation function, viscoelasticity",

author = "N. Tatar",

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

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AU - Tatar, N.

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

PY - 2013

Y1 - 2013

N2 - In this paper we consider a Kirchhoff type viscoelastic problem, and prove uniform stability of the system. We do not rely on the dissipativity of the system or the boundedness of the energy as in the previous treatments. There appears a quadratic term which we cannot estimate by the initial energy as our system is not clearly dissipative in advance.

AB - In this paper we consider a Kirchhoff type viscoelastic problem, and prove uniform stability of the system. We do not rely on the dissipativity of the system or the boundedness of the energy as in the previous treatments. There appears a quadratic term which we cannot estimate by the initial energy as our system is not clearly dissipative in advance.

KW - Exponential decay

KW - Kirchhoff equation

KW - memory term

KW - relaxation function

KW - viscoelasticity

UR - https://www.scopus.com/pages/publications/84893602452

U2 - 10.3103/S1068362313060058

DO - 10.3103/S1068362313060058

M3 - Article

AN - SCOPUS:84893602452

SN - 1068-3623

VL - 48

SP - 285

EP - 296

JO - Journal of Contemporary Mathematical Analysis

JF - Journal of Contemporary Mathematical Analysis

IS - 6

ER -

On a non-dissipative Kirchhoff viscoelastic problem

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this