Geodesic
Optimal control of a~rigidity parameter of thin inclusions in elastic bodies with curvilinear cracks
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 1, pp. 135-149

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The paper concerns an optimal control problem for a 2D elastic body with a thin rigid inclusion and a crack. Inequality type boundary conditions are imposed at the crack faces to provide a mutual non-penetration between the crack faces. The cost functional characterizes a derivative of the energy functional with respect to the crack length. A rigidity of the inclusion is considered as a control function. The main result consists in a proof of the solution existence to the optimal control problem.
Keywords: crack, thin inclusion, nonlinear boundary conditions, optimal control, derivative of energy functional. 
@article{VNGU_2013_13_1_a11,
     author = {V. V. Shcherbakov},
     title = {Optimal control of a~rigidity parameter of thin inclusions in elastic bodies with curvilinear cracks},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {135--149},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2013_13_1_a11/}
}
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V. V. Shcherbakov. Optimal control of a~rigidity parameter of thin inclusions in elastic bodies with curvilinear cracks. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 1, pp. 135-149. http://geodesic.mathdoc.fr/item/VNGU_2013_13_1_a11/