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

摘要

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. (C) 2021 Elsevier B.V. All rights reserved.