TY - JOUR
T1 - Optimal Control of a Quasistatic Frictional Contact Problem with History-Dependent Operators
AU - Li , Yujie
AU - Cheng , Xiaoliang
AU - Wang , Xilu
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 29
EP - 46
PY - 2022
DA - 2022/11
SN - 20
DO - http://doi.org/ 10.4208/ijnam2023-1002
UR - https://global-sci.org/intro/article_detail/ijnam/21203.html
KW - Variational inequality, contact problem, history-dependent operator, optimal control.
AB - <p style="text-align: justify;">In this paper, we are concerned with an optimal control problem of a quasistatic
frictional contact model with history-dependent operators. The contact boundary of the model is
divided into two parts where different contact conditions are specified. For the contact problem,
we first derive its weak formulation and prove the existence and uniqueness of the solution to the
weak formulation. Then we give a priori estimate of the unique solution and prove a continuous
dependence result for the solution map. Finally, an optimal control problem that contains boundary and initial condition controls is proposed, and the existence of optimal solutions to the control
problem is established.</p>