Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 118, pp. 1-15.

Title: Analysis of electro-viscoelastic antiplane contact problem
       with total slip rate dependent friction

Author: Mohamed Dalah (Univ. Mentouri de Constantine, Algiria)

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
 electro-viscoelastic 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 time-dependent 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 fixed-point
 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;
           electro-viscoelastic law; fixed point;  weak solution; 
	   variational inequality; Tresca's friction law.