On some optimal control problem for a parabolic system with boundary condition involving a time-varying lag

1992 ◽  
Vol 9 (2) ◽  
pp. 131-146 ◽  
Author(s):  
ADAM KOWALEWSKI ◽  
JAN DUDA
Keyword(s):  
Boundary Condition ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Parabolic System ◽  
Time Varying

scholarly journals An Approximation of Solutions for the Problem with Quasistatic Contact in the Case of Dry Friction

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 904
Author(s):  
Nicolae Pop ◽  
Miorita Ungureanu ◽  
Adrian I. Pop
Keyword(s):  
Boundary Condition ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Displacement Field ◽  
Dry Friction ◽  
Control Variable ◽  
Traction Force ◽  
The State ◽  
State System

In this paper, we discuss the question of finding an optimal control for the solutions of the problem with dry friction quasistatic contact, in the case that the friction law is modeled by a nonlocal version of Coulomb’s law. In order to get the necessary optimality conditions, we use some regularization techniques, and this leads us to a problem of control for an inequality of the variational type. The optimal control problem consists, in our case, of minimizing a sequence of optimal control problems, where the control variable is given by a Neumann-type boundary condition. The state system is represented by a limit of a sequence, whose terms are obtained from the discretization, in time with finite difference and space with the finite element method of a regularized quasistatic contact problem with Coulomb friction. The purpose of this optimal control problem is that the traction force (the control variable) acting on one side of the boundary (the Neumann boundary condition) of the elastic body produces a displacement field (the state system solution) close enough to the imposed displacement field, and the traction force from the boundary remains small enough.

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