Asymptotic behaviour for the vibrations modeled by the standard linear solid model with a thermal effect

Margareth S. Alves; Celene Buriol; Marcio V. Ferreira; Jaime E.Muñoz Rivera; Mauricio Sepúlveda; Octavio Vera

doi:10.1016/j.jmaa.2012.10.019

Asymptotic behaviour for the vibrations modeled by the standard linear solid model with a thermal effect

Margareth S. Alves
, Celene Buriol
, Marcio V. Ferreira
, Jaime E.Muñoz Rivera
, Mauricio Sepúlveda
, Octavio Vera

Universidade Federal de Viçosa
Universidade Federal de Santa Maria
LNCC/MCT
Universidad de Concepción
Departamento Matemática. UBB

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

36 Scopus citations

Abstract

We consider vibrations modeled by the standard linear solid model of viscoelasticity which are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction. We show that the exponential stability under the Fourier law of heat conduction holds. In order to obtain the asymptotic behaviour we use multiplier techniques.

Original language	English
Pages (from-to)	472-479
Number of pages	8
Journal	Journal of Mathematical Analysis and Applications
Volume	399
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2012.10.019
State	Published - 15 Mar 2013
Externally published	Yes

Keywords

Asymptotic behaviour
C0-semigroup
Coupled system of thermoviscoelastic equations

Access to Document

10.1016/j.jmaa.2012.10.019

Cite this

@article{bb1612e67ebb43cfb15e0acde86c8bb5,

title = "Asymptotic behaviour for the vibrations modeled by the standard linear solid model with a thermal effect",

abstract = "We consider vibrations modeled by the standard linear solid model of viscoelasticity which are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction. We show that the exponential stability under the Fourier law of heat conduction holds. In order to obtain the asymptotic behaviour we use multiplier techniques.",

keywords = "Asymptotic behaviour, C0-semigroup, Coupled system of thermoviscoelastic equations",

author = "Alves, \{Margareth S.\} and Celene Buriol and Ferreira, \{Marcio V.\} and Rivera, \{Jaime E.Mu{\~n}oz\} and Mauricio Sep{\'u}lveda and Octavio Vera",

year = "2013",

month = mar,

day = "15",

doi = "10.1016/j.jmaa.2012.10.019",

language = "English",

volume = "399",

pages = "472--479",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

number = "2",

}

TY - JOUR

T1 - Asymptotic behaviour for the vibrations modeled by the standard linear solid model with a thermal effect

AU - Alves, Margareth S.

AU - Buriol, Celene

AU - Ferreira, Marcio V.

AU - Rivera, Jaime E.Muñoz

AU - Sepúlveda, Mauricio

AU - Vera, Octavio

PY - 2013/3/15

Y1 - 2013/3/15

N2 - We consider vibrations modeled by the standard linear solid model of viscoelasticity which are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction. We show that the exponential stability under the Fourier law of heat conduction holds. In order to obtain the asymptotic behaviour we use multiplier techniques.

AB - We consider vibrations modeled by the standard linear solid model of viscoelasticity which are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction. We show that the exponential stability under the Fourier law of heat conduction holds. In order to obtain the asymptotic behaviour we use multiplier techniques.

KW - Asymptotic behaviour

KW - C0-semigroup

KW - Coupled system of thermoviscoelastic equations

UR - https://www.scopus.com/pages/publications/84870053184

U2 - 10.1016/j.jmaa.2012.10.019

DO - 10.1016/j.jmaa.2012.10.019

M3 - Article

AN - SCOPUS:84870053184

SN - 0022-247X

VL - 399

SP - 472

EP - 479

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Asymptotic behaviour for the vibrations modeled by the standard linear solid model with a thermal effect

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this