IJPAM: Volume 104, No. 1 (2015)

ANALYSIS AND STUDY OF WEAK SOLUTION OF
ANTIPLANE ELECTRO-VISCOELASTIC PROBLEM

Ammar Derbazi$^1$, Amar Megrous$^2$, Mohamed Dalah$^3$
$^1$Department of Mathematics
Faculty of MI
Ammar Derbazi University Bachir El Ibrahimi
Bordj Bou Arreridj, 34 000, ALGERIA
$^2$Amar Megrous Ecole Préparatoire en Sciences Economiques
Commerciales et Sciences de Gestion EPSE-CSG of Constantine
25 000, ALGERIA
$^3$Department of Mathematics
Faculty of Sciences
Mohamed Dalah University of Frères Mentouri Constantine
Constantine, 25000, ALGERIA


Abstract. In this work we study a mathematical model which describes the antiplane shear deformation of a cylinder in frictionless contact with a rigid foundation. The material is assumed to be electro-viscoelastic with long-term memory, and the friction is modeled with Tresca's law and the foundation is assumed to be electrically conductive. First we derive the classical variational formulation of the model which is given by a system coupling an evolutionary variational equality for the displacement field and a time-dependent variational equation for the potential field. Then we prove the existence of a unique weak solution to the model. Moreover, the Proof is based on arguments of evolution equations and by using the Banach fixed-point theorem.

Received: April 29, 2015

AMS Subject Classification: 74M10, 74F15, 74G25, 49J40

Key Words and Phrases: Tresca's friction, antiplane shears deformation, electro-viscoelastic material, variational inequality, weak solution, fixed point

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DOI: 10.12732/ijpam.v104i1.8 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 104
Issue: 1
Pages: 87 - 106


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