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A two-dimensional model describing the equilibrium state of a cracked inhomogeneous body with a rigid circular inclusion is investigated. The body is assumed to have a crack that reaches the boundary of the rigid inclusion. We assume that the Signorini condition, ensuring non-penetration of the crack faces, is satisfied. We analyze the dependence of solutions on the radius of rigid
inclusion. The existence of a solution of the optimal control problem is proven. For this problem, a cost functional is defined by an arbitrary continuous functional, with the radius of inclusion chosen as the control parameter.
| Acceptance Date | Mar 22, 2018 |
|---|---|
| Publication Date | Apr 11, 2018 |
| Journal | Zeitschrift fur angewandte Mathematik und Physik |
| Print ISSN | 0044-2275 |
| Publisher | Springer Verlag |
| DOI | https://doi.org/10.1007/s00033-018-0949-2 |
| Keywords | variational inequality, optimal control problem, nonpenetration, non-linear boundary conditions, crack, rigid inclusion |
| Publisher URL | https://doi.org/10.1007/s00033-018-0949-2 |
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