Optimal control and a system of quasi-variational inequalities

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 06 آذر 1404

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.92539.1611

نویسنده

Justyna Ogorzaly^*

Institute of Mathematics and Cryptology, Military University of Technology, ul. gen. S. Kaliskiego 2, Warsaw, Poland.

چکیده

In this paper, we consider the system of two quasi-variational inequalities. First, we show that such a system has a unique solution. Next, we will study a convergence result with respect to the set of constraints. This result is important in the study of the optimal control problem associated with the considered system. Next, we formulate an optimal control problem for which we prove the existence of an optimal solution, together with the convergence of optimal control pairs. Finally, we apply our results in the study of the contact problem with thermal effect and boundary conditions, including the Signorini-type condition and normal compliance contact condition coupled with the Coulomb friction law.

کلیدواژه‌ها

quasi-variational inequality؛ Mosco convergence؛ optimal control؛ thermal effect