Existence and uniqueness of the weak solution for a contact problem
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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.
Share and Cite
ISRP Style
Amar Megrous, Ammar Derbazi, Mohamed Dalah, Existence and uniqueness of the weak solution for a contact problem, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 1, 186--199
AMA Style
Megrous Amar, Derbazi Ammar, Dalah Mohamed, Existence and uniqueness of the weak solution for a contact problem. J. Nonlinear Sci. Appl. (2016); 9(1):186--199
Chicago/Turabian Style
Megrous, Amar, Derbazi, Ammar, Dalah, Mohamed. "Existence and uniqueness of the weak solution for a contact problem." Journal of Nonlinear Sciences and Applications, 9, no. 1 (2016): 186--199
Keywords
- Weak solution
- variational formulation
- Banach fixed point theorem
- variational inequality
- evolution equations.
MSC
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