We study the optimal control problem for nonlinear mathematical models describing the equilibrium state of an inhomogeneous body, where the nonlinearity is caused by the Signorini contact condition. We establish the solvability of the optimal control problem and prove that the equilibrium problem for an elastic body with two joined rigid inclusions is the limit for a family of equilibrium problems for bodies with two separate inclusions.
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Translated from Problemy Matematicheskogo Analiza 122, 2023, pp. 61-67.
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Lazarev, N.P., Semenova, G.M. The Problem of the Location of an Inclusion in a Two-Dimensional Elastic Body with Two Thin Rigid Inclusions. J Math Sci 270, 571–578 (2023). https://doi.org/10.1007/s10958-023-06368-3
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DOI: https://doi.org/10.1007/s10958-023-06368-3