Existence and uniqueness of the weak solution for a contact problem

Volume 9, Issue 1, pp 186--199 http://dx.doi.org/10.22436/jnsa.009.01.17

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Authors

Amar Megrous - Department of Mathematics, EPSE-CSG, Constantine 25 000, Algeria. Ammar Derbazi - Faculty of MI, Department of Mathematics, University Bordj BBA, Bordj BBA 34 000, Algeria. Mohamed Dalah - Faculty of Exactes Sciences: FSE, Department of Mathematics, University Mentouri of Constantine, Constantine 25 017, Algeria.

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, 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, a time-dependent variational equation for the potential field and a differential equation for the bounding field. Then we prove the existence of a unique weak solution for the model. The proof is based on arguments of evolution equations and the Banach fixed point theorem.

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Keywords

• Weak solution
• variational formulation
• Banach fixed point theorem
• variational inequality
• evolution equations.

MSC

•  74M10
•  74F15
•  74G25
•  49J40

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