Electron. J. Diff. Equ.,
Vol. 2009(2009), No. 118, pp. 115.
Analysis of electroviscoelastic antiplane contact problem
with total slip rate dependent friction
Mohamed Dalah
Abstract:
We consider a mathematical model which describes the antiplane
shear deformation of a cylinder in frictional contact with a rigid
foundation. The contact is bilateral and is modelled with a total
slip rate dependent friction law. The material is assumed to be
electroviscoelastic and the foundation is assumed to be
electrically conductive. First, we describe the classical
formulation for the antiplane problem and we give the
corresponding variational formulation which is given by a system
coupling an evolutionary variational equality for the displacement
field and a timedependent variational equation for the electric
potential field. Then we prove the existence of a unique weak
solution to the model. The proof is based on arguments of
variational inequalities and by using the Banach fixedpoint
Theorem.
Submitted March 3, 2009. Published September 27, 2009.
Math Subject Classifications: 74M10, 74F15, 74G25, 49J40.
Key Words: Antiplane problem; total slip rate dependent friction law;
electroviscoelastic law; fixed point; weak solution;
variational inequality; Tresca's friction law.
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Mohamed Dalah
Laboratoire Modélisation Mathématiques et Simulation (LMMS)
Département de Matématiques, Faculté des Sciences
Université Mentouri de Constantine
Route Ain ElBey Zerzara, 25 000 Constantine, Algiria
email: mdalah17@yahoo.fr

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