Abstract
In this paper we investigate the optimal control problem for set-valued quasivariational inequality with unilateral constraints. Under suitable conditions, we prove that the solution to the current optimal control problem converges to a solution to old control problems. By way of application, we utilize our results presented in the paper to study the optimal control associated with boundary value problems which is described by frictional contact problems and a stationary heat transfer problem with unilateral constraints.
Highlights
The theory of variational techniques refers to the tool for estimating the appropriate auxiliary function that attains a minimum
Since so many key results in mathematics, in the analysis, have their origins in the physical sciences, it is entirely natural that they can be associated in one way or another to variational techniques
Results in the study of optimal control for variational inequalities have been addressed in several research papers, including [10,11,12,13,14,15,16] and the applications in mechanics, see [17,18,19]
Summary
The theory of variational techniques refers to the tool for estimating the appropriate auxiliary function that attains a minimum This can be conceived as a mathematical model of the concept of the least action in physics and engineering. Results in the study of optimal control for variational inequalities have been addressed in several research papers, including [10,11,12,13,14,15,16] and the applications in mechanics, see [17,18,19] These are some more references of optimal control in mechanics, physics and engineering where we can see the discussion, see [20,21,22,23,24,25]. We deploy our results to demonstrate the frictional contact of an elastic material with a rigid-deformable foundation and a stationary heat transfer boundary value problem with unilateral constraints
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