On the uniform decay in Cauchy viscoelastic problems

Mohammad Kafini

doi:10.1007/s13370-011-0020-3

On the uniform decay in Cauchy viscoelastic problems

Mohammad Kafini^*

^*Corresponding author for this work

Department of Mathematics

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

5 Scopus citations

Abstract

In this paper we consider a linear Cauchy viscoelastic problem with an external source term. We show that, for compactly supported initial data and for an exponentially decaying relaxation function, the decay of the first energy of solution is polynomial. The finite-speed propagation is used to compensate for the lack of Poincaré's inequality in ℝⁿ.

Original language	English
Pages (from-to)	85-97
Number of pages	13
Journal	Afrika Matematika
Volume	23
Issue number	1
DOIs	https://doi.org/10.1007/s13370-011-0020-3
State	Published - Apr 2012

Keywords

Cauchy problem
Compactly supported
Decay
Hyperbolic
Relaxation function
Viscoelastic

ASJC Scopus subject areas

General Mathematics

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10.1007/s13370-011-0020-3

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title = "On the uniform decay in Cauchy viscoelastic problems",

abstract = "In this paper we consider a linear Cauchy viscoelastic problem with an external source term. We show that, for compactly supported initial data and for an exponentially decaying relaxation function, the decay of the first energy of solution is polynomial. The finite-speed propagation is used to compensate for the lack of Poincar{\'e}'s inequality in ℝn.",

keywords = "Cauchy problem, Compactly supported, Decay, Hyperbolic, Relaxation function, Viscoelastic",

author = "Mohammad Kafini",

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AB - In this paper we consider a linear Cauchy viscoelastic problem with an external source term. We show that, for compactly supported initial data and for an exponentially decaying relaxation function, the decay of the first energy of solution is polynomial. The finite-speed propagation is used to compensate for the lack of Poincaré's inequality in ℝn.

KW - Cauchy problem

KW - Compactly supported

KW - Decay

KW - Hyperbolic

KW - Relaxation function

KW - Viscoelastic

UR - https://www.scopus.com/pages/publications/84873490957

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DO - 10.1007/s13370-011-0020-3

M3 - Article

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SN - 1012-9405

VL - 23

SP - 85

EP - 97

JO - Afrika Matematika

JF - Afrika Matematika

IS - 1

ER -

On the uniform decay in Cauchy viscoelastic problems

Abstract

Keywords

ASJC Scopus subject areas

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