Dalah, Mohamed; Sofonea, Mircea Antiplane frictional contact of electro-viscoelastic cylinders. (English) Zbl 1139.74039 Electron. J. Differ. Equ. 2007, Paper No. 161, 14 p. (2007). Summary: We study a mathematical model that describes the antiplane shear deformation of a cylinder in frictional contact with a rigid foundation. The material is assumed to be electro-viscoelastic, the process is quasistatic, friction is modelled with Tresca law, and the foundation is assumed to be electrically conductive. We derive a variational formulation of the model which is in a form of a system coupling a first-order evolutionary variational inequality for the displacement field with 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 evolutionary variational inequalities and fixed points of operators. Also, we investigate the behavior of the solution as the viscosity converges to zero and prove that it converges to the solution of the corresponding electro-elastic antiplane contact problem. Cited in 4 Documents MSC: 74M15 Contact in solid mechanics 74M10 Friction in solid mechanics 74F15 Electromagnetic effects in solid mechanics 74H20 Existence of solutions of dynamical problems in solid mechanics 74H25 Uniqueness of solutions of dynamical problems in solid mechanics 49J40 Variational inequalities Keywords:Tresca friction law; evolutionary variational inequality; weak solution PDFBibTeX XMLCite \textit{M. Dalah} and \textit{M. Sofonea}, Electron. J. Differ. Equ. 2007, Paper No. 161, 14 p. (2007; Zbl 1139.74039) Full Text: EuDML EMIS