Abstract
In this paper, we consider the behaviour of solutions to a class of fully history-dependent variational-hemivariational inequalities with respect to the perturbation of the data. First, the existence and uniqueness of the solution to a class of fully history-dependent variational-hemivariational inequalities is obtained by using a fixed point theorem. Second, we obtain continuous dependence result of solutions with respect to all the data of variational-hemivariational inequalities. Meanwhile, the convergence results of the solutions for the special case of abstract variational inequalities are also given. Finally, to illustrate our main results, we consider a class of viscoelastic contact problem with a long memory. By using our abstract result, we get the continuous dependence of the solutions to frictional contact problem with respect to all the data.
Acknowledgments
The authors are grateful to the referees for their careful reading of the manuscript and valuable comments. The authors thank the help from the editor too. Furi Guo, JinRong Wang and Liang Lu: Writing-original draft; Writing-review and editing. JinRong Wang: Supervision.
Disclosure statement
No potential conflict of interest was reported by the author(s).