@article{Medjerab Samia and Aissaoui Adel_2024, title={Solvability of a coupled hemivariational system in anti planes hear}, volume={120}, url={https://utilitasmathematica.com/index.php/Index/article/view/1950}, abstractNote={<p>In this research paper, we present some results on the solvability of the evolutionary system constituting two types of hemivariational inequalities in the study of a piezoelectric frictional contact problem with specific subdifferential boundary conditions. Here, the modeling of quasistatic contact processes is described with linear electro-viscoelastic behavior in the case of antiplane shear deformation, where the foundation is assumed conductive.&nbsp; The novelty of this modeling is the dependence of the friction force on the total slip-rate with electrical effects, while the conductivity coefficient only depends on the total slip rate. We use a variational formula to express this friction model, which is a coupled system composed of two hemivariational inequalities, one of which is specific to the displacement field and the other is time-dependent for the electric potential field. Then, we show that this mathematical model has a unique weak solution, the proof is based on results of evolutionary and history-dependent inclusions under certain assumptions.</p> <p><strong>&nbsp;</strong></p>}, journal={Utilitas Mathematica }, author={Medjerab Samia and Aissaoui Adel}, year={2024}, month={May}, pages={1278–1297} }