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Volume 20, Issue 1
Optimal Control of a Quasistatic Frictional Contact Problem with History-Dependent Operators

Yujie Li, Xiaoliang Cheng & Xilu Wang

DOI: 10.4208/ijnam2023-1002

Int. J. Numer. Anal. Mod., 20 (2023), pp. 29-46.

Published online: 2022-11

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  • Abstract

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.

  • Keywords

Variational inequality, contact problem, history-dependent operator, optimal control.

  • AMS Subject Headings

47J20, 49J20, 74M15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-20-29, author = {Li , YujieCheng , Xiaoliang and Wang , Xilu}, title = {Optimal Control of a Quasistatic Frictional Contact Problem with History-Dependent Operators}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {20}, number = {1}, pages = {29--46}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/ 10.4208/ijnam2023-1002}, url = {http://global-sci.org/intro/article_detail/ijnam/21203.html} }
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 -

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.

Li , YujieCheng , Xiaoliang and Wang , Xilu. (2022). Optimal Control of a Quasistatic Frictional Contact Problem with History-Dependent Operators. International Journal of Numerical Analysis and Modeling. 20 (1). 29-46. doi: 10.4208/ijnam2023-1002
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