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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2023. Vol 43

Optimal Location Problem for Composite Bodies with Separate and Joined Rigid Inclusions

Author(s)
Nyurgun P. Lazarev1, Galina M. Semenova1

1North-Eastern Federal University, Yakutsk, Russian Federation

Abstract
Nonlinear mathematical models describing an equilibrium state of composite bodies which may come into contact with a fixed non-deformable obstacle are investigated. We suppose that the composite bodies consist of an elastic matrix and one or two built-in volume (bulk) rigid inclusions. These inclusions have a rectangular shape and one of them can vary its location along a straight line. Considering a location parameter as a control parameter, we formulate an optimal control problem with a cost functional specified by an arbitrary continuous functional on the solution space. Assuming that the location parameter varies in a given closed interval, the solvability of the optimal control problem is established. Furthermore, it is shown that the equilibrium problem for the composite body with joined two inclusions can be considered as a limiting problem for the family of equilibrium problems for bodies with two separate inclusions.
About the Authors

Nyurgun P. Lazarev, Dr. Sci. (Phys.–Math.), North-Eastern Federal University, Yakutsk, 677000, Russian Federation, nyurgun@ngs.ru

Galina M. Semenova, Cand. Sci. (Ped.), Assoc. Prof., North-Eastern Federal University, Yakutsk, 677000, Russian Federation, sgm.08@yandex.ru

For citation
Lazarev N. P., Semenova G. M. Optimal Location Problem for Composite Bodies with Separate and Joined Rigid Inclusions. The Bulletin of Irkutsk State University. Series Mathematics, 2023, vol. 43, pp. 19–30. https://doi.org/10.26516/1997-7670.2023.43.19
Keywords
optimal control problem, composite body, Signorini conditions, rigid inclusion, location.
UDC
517.97
MSC
49J40, 49J20
DOI
https://doi.org/10.26516/1997-7670.2023.43.19
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