Optimal Control of Quasivariational Inequalities with Applications to Contact Mechanics

Mircea Sofonea ()
Additional contact information
Mircea Sofonea: University of Perpignan Via Domitia, Laboratoire de Mathématiques et Physique

Chapter Chapter 13 in Current Trends in Mathematical Analysis and Its Interdisciplinary Applications, 2019, pp 445-489 from Springer

Abstract: Abstract This chapter deals with the optimal control of a class of elliptic quasivariational inequalities. We start with an existence and uniqueness result for such inequalities. Then we state an optimal control problem, list the assumptions on the data and prove the existence of optimal pairs. We proceed with a perturbed control problem for which we state and prove a convergence result, under general conditions. Further, we present a relevant particular case for which these conditions are satisfied and, therefore, our convergence result works. Finally, we illustrate the use of these abstract results in the study of a mathematical model which describes the equilibrium of an elastic body in frictional contact with an obstacle, the so-called foundation. The process is static and the contact is modeled with normal compliance and unilateral constraint, associated with the Coulomb’s law of dry friction. We prove the existence, uniqueness, and convergence results together with the corresponding mechanical interpretation. We illustrate these results in the study of a one-dimensional example. Finally, we end this chapter with some concluding remarks.

Keywords: Quasivariational inequality; Optimal pair; Optimal control; Convergence results; Frictional contact; Unilateral constraint; Weak solution (search for similar items in EconPapers)
Date: 2019
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-15242-0_13

Ordering information: This item can be ordered from
http://www.springer.com/9783030152420

DOI: 10.1007/978-3-030-15242-0_13

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().