A new class of differential nonlinear system involving parabolic variational and history-dependent hemi-variational inequalities arising in contact mechanics

Abstract This paper is devoted to study a new nonlinear system involving a parabolic variational inequality, a history-dependent hemi-variational inequality and a differential equation in Banach spaces. By employing the surjectivity argument and Banach’s fixed point theorem, we derive a unique solvability theorem for such a problem under some mild conditions. Moreover, the main results are applied to obtain the unique solvability of a long memory elastic frictional contact problem with wear and damage. Finally, we use the fully discrete scheme to approximate the contact problem and provide the error estimates for numerical solutions.

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