# The weak solution of an antiplane contact problem for electro-viscoelastic materials with long-term memory

• Volume: 61, Issue: 3, page 339-358
• ISSN: 0862-7940

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## Abstract

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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 with 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 on the Banach fixed-point theorem.

## How to cite

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Derbazi, Ammar, Dalah, Mohamed, and Megrous, Amar. "The weak solution of an antiplane contact problem for electro-viscoelastic materials with long-term memory." Applications of Mathematics 61.3 (2016): 339-358. <http://eudml.org/doc/276996>.

@article{Derbazi2016,
abstract = {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 with 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 on the Banach fixed-point theorem.},
author = {Derbazi, Ammar, Dalah, Mohamed, Megrous, Amar},
journal = {Applications of Mathematics},
keywords = {weak solution; variational formulation; antiplane shear deformation; electro-viscoelastic material; Tresca's friction; fixed point; variational inequality; weak solution; variational formulation; antiplane shear deformation; electro-viscoelastic material; Tresca's friction; fixed point; variational inequality},
language = {eng},
number = {3},
pages = {339-358},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The weak solution of an antiplane contact problem for electro-viscoelastic materials with long-term memory},
url = {http://eudml.org/doc/276996},
volume = {61},
year = {2016},
}

TY - JOUR
AU - Derbazi, Ammar
AU - Dalah, Mohamed
AU - Megrous, Amar
TI - The weak solution of an antiplane contact problem for electro-viscoelastic materials with long-term memory
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 3
SP - 339
EP - 358
AB - 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 with 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 on the Banach fixed-point theorem.
LA - eng
KW - weak solution; variational formulation; antiplane shear deformation; electro-viscoelastic material; Tresca's friction; fixed point; variational inequality; weak solution; variational formulation; antiplane shear deformation; electro-viscoelastic material; Tresca's friction; fixed point; variational inequality
UR - http://eudml.org/doc/276996
ER -

## References

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