Penalty method for a class of differential nonlinear system arising in contact mechanics

Abstract The main goal of this paper is to study a class differential nonlinear system involving parabolic variational and history-dependent hemivariational inequalities in Banach spaces by using the penalty method. We first construct penalized problem for such then derive existence uniqueness its solution obtain an approximating sequence system. Moreover, we prove strong convergence obtained original when parameter converges zero. Finally, apply result long-memory elastic frictional contact with wear damage mechanics. First part title : Introduction Second Preliminaries Third Convergence (1.1) Fourth An application