Geodesic
Optimal control of the location of a thin rigid inclusion in the equilibrium problem of an inhomogeneous two-dimensional body with a crack
Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 1, pp. 53-62

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Under study is some two-dimensional model describing equilibrium of a composite solid with a thin rigid inclusion and a crack. A boundary condition of Signorini's type is prescribed on the crack curve. For a family of corresponding variational problems, the dependence is analyzed of their solutions on the parameter characterizing the location of the rigid inclusion. The existence of solution of the optimal control problem is proved. For this problem, the quality functional is defined with the help of an arbitrary continuous functional on the solution space, while the location of the inclusion is chosen as the control parameter.
Keywords: variational inequality, optimal control problem, nonpenetration condition, nonlinear boundary conditions, crack, rigid inclusion. 
@article{SJIM_2019_22_1_a5,
     author = {N. P. Lazarev and G. M. Semenova},
     title = {Optimal control of the location of a thin rigid inclusion in the equilibrium problem of an inhomogeneous two-dimensional body with a crack},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {53--62},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2019_22_1_a5/}
}
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N. P. Lazarev; G. M. Semenova. Optimal control of the location of a thin rigid inclusion in the equilibrium problem of an inhomogeneous two-dimensional body with a crack. Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 1, pp. 53-62. http://geodesic.mathdoc.fr/item/SJIM_2019_22_1_a5/