ABSTRACT
In this paper, we consider a dynamic viscoelastic contact problem with friction and wear, and describe it as a system of nonlinear partial differential equations. We formulate the previous problem as a hyperbolic quasi-variational inequality by employing the variational method. We adopt the Rothe method to show the existence and uniqueness of solution for the hyperbolic quasi-variational inequality under mild conditions. We also give a fully discrete scheme for solving the hyperbolic quasi-variational inequality and obtain error estimates for the fully discrete scheme.
Acknowledgments
The authors are grateful to Professor M. Sofonea for his valuable comments and suggestions. We also thank the editor and reviewers for their constructive comments, which helps us to improve the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.